Imam Sadiq --peace be upon him-- was asked about a verse in which Allah talks about those with sick hearts. He answered that the heart is sick when someone tends to wrong and dislikes committing the good deeds. And this can also be seen from here:
وَلَوِ اتَّبَعَ الْحَقُّ أَهْوَاءَهُمْ لَفَسَدَتِ السَّمَاوَاتُ
وَالْأَرْضُ وَمَن فِيهِنَّ بَلْ أَتَيْنَاهُم بِذِكْرِهِمْ فَهُمْ عَن
If the Truth had been in accord with their desires, truly the heavens
and the earth, and all beings therein would have been in confusion and
corruption! Nay, We have sent them their admonition, but they turn
away from their admonition. [23:71]
And heart in Islam is very much close to the concept of intellect, rather than a limb in the breast. Indeed heart is the base for intellectual power like brain is the base for mind and thinking:
أَفَلَمْ يَسِيرُوا فِي الْأَرْضِ فَتَكُونَ لَهُمْ قُلُوبٌ
يَعْقِلُونَ بِهَا أَوْ آذَانٌ يَسْمَعُونَ بِهَا فَإِنَّهَا لَا
تَعْمَى الْأَبْصَارُ وَلَٰكِن تَعْمَى الْقُلُوبُ الَّتِي فِي
So have they not traveled through the earth and have hearts by which
to reason and ears by which to hear? For indeed, it is not eyes that
are blinded, but blinded are the hearts which are within the
That heart is called to be within breast also shows that the breast here is not the breast as a part of body, like Moses --peace be upon him-- asked Allah in [20:25] that "... رَبِّ اشْرَحْ لِي صَدْرِي" which implies "... My Lord, expand for me my breast". Although the similarity of names and relations show a relation between the heart in Quran and the limb within the breast, but that needs another discussion, here we only aim to say if Allah talks about people with sick hearts what He means, that this disease will affect their reasoning, e.g. they would not be able to recognize reason from justification and the fallacy, or that their reasoning will always have a preferred direction, inclination toward wrongness.
Imam Husain --peace be upon him-- on the other hand has advised us to follow and obey the rules of religion for the health recovery of our sick hearts. Also note that the holy Quran introduces the guidances of Quran as healing for our hearts:
يَا أَيُّهَا النَّاسُ قَدْ جَاءَتْكُم مَّوْعِظَةٌ مِّن رَّبِّكُمْ
وَشِفَاءٌ لِّمَا فِي الصُّدُورِ وَهُدًى وَرَحْمَةٌ لِّلْمُؤْمِنِينَ
O mankind! there hath come to you a direction from your Lord and a
healing for the (diseases) in your hearts,- and for those who believe,
a guidance and a Mercy. [10:57]
وَنُنَزِّلُ مِنَ الْقُرْآنِ مَا هُوَ شِفَاءٌ وَرَحْمَةٌ
لِّلْمُؤْمِنِينَ ۙ وَلَا يَزِيدُ الظَّالِمِينَ إِلَّا خَسَارًا
We send down (stage by stage) in the Qur'an that which is a healing
and a mercy to those who believe: to the unjust it causes nothing but
loss after loss. [since the believers would obey and the unjust
people would disobey and withstand the rules and guidance of Allah] [17:82]
When someone has a healthy heart he will recognize the good and bad based on Fitrah (فطرة), the very intrinsic nature of human being, or according to its definition from Quran:
... فِطْرَتَ اللَّهِ الَّتِي فَطَرَ النَّاسَ عَلَيْهَا لَا تَبْدِيلَ
لِخَلْقِ اللَّهِ ذَٰلِكَ الدِّينُ الْقَيِّمُ وَلَٰكِنَّ أَكْثَرَ
النَّاسِ لَا يَعْلَمُونَ
... Allah's handiwork according to the pattern on which He has made
mankind: no change (let there be) in the work (wrought) by Allah: that
is the standard Religion: but most among mankind understand not.
That is, the whole list of "goods and bads" is carved in our Fitrah, and this Fitrah will never change through the course of time, from one generation to another, as long as someone is born as human his Fitrah would be the same, although be covered and not visible when our heart get sick. However, most among the mankind don't know this very clear fact, they have always discrepancies of ideas and understandings because we have lost our Fitrah deep in our insides. We just cannot see it. We cannot feel our deep hate of any wrong deed and our pure and deep like of the good deeds since we are sick. A sick person may smell a very good smelling flower and yet be teased of the smell, but that's because he is sick, and if he recovers his health he will again find that smelling one of a very good kind. Therefore, intrinsically there is no need to many rules and remarks at all. In another Hadeeth it is stated that once a man came from the desert to the holy prophet --peace be upon him-- and asked to teach him making Vozu' (cleaning required before prayer, which implies acquiring illumination before to visit Allah in the prayer). The holy prophet only told him to wash his face and then his hands, and then wipe over his head and feet. The man left and the prophet's companion gathered around the holy prophet to ask why he didn't tell the man any among many details of making Vozu'? The holy prophet --peace be upon him-- asked his companions to go after the man and see how he cleans himself for prayer. They went and saw he made Vozu' exactly correct with all its details. This shows the man's heart was not sick so that he could easily do this base on his Fitrah and intellectual power. Also let me bring you another example from Quran. The Israelite were ordered to sacrifice a cow. They didn't want to do so on their own will unless they have no other choice to do so, so that if it is not quite necessary then maybe they will be let free not to kill the cow; so they were all the times making excuses by asking about many details, its color and blow blow, until Allah gave them all the details and they had no other excuse to withstand the order of Allah, so that they sacrificed the cow but then Allah, the narrator who knows all the apparent and hidden facts, adds that they were going not to kill the cow if they could!
وَإِذْ قَالَ مُوسَىٰ لِقَوْمِهِ إِنَّ اللَّهَ يَأْمُرُكُمْ أَن
تَذْبَحُوا بَقَرَةً ۖ قَالُوا أَتَتَّخِذُنَا هُزُوًا ۖ قَالَ أَعُوذُ
بِاللَّهِ أَنْ أَكُونَ مِنَ الْجَاهِلِينَ / قَالُوا ادْعُ لَنَا
رَبَّكَ يُبَيِّن لَّنَا مَا هِيَ ۚ قَالَ إِنَّهُ يَقُولُ إِنَّهَا
بَقَرَةٌ لَّا فَارِضٌ وَلَا بِكْرٌ عَوَانٌ بَيْنَ ذَٰلِكَ ۖ
فَافْعَلُوا مَا تُؤْمَرُونَ / قَالُوا ادْعُ لَنَا رَبَّكَ يُبَيِّن
لَّنَا مَا لَوْنُهَا ۚ قَالَ إِنَّهُ يَقُولُ إِنَّهَا بَقَرَةٌ
صَفْرَاءُ فَاقِعٌ لَّوْنُهَا تَسُرُّ النَّاظِرِينَ / قَالُوا ادْعُ
لَنَا رَبَّكَ يُبَيِّن لَّنَا مَا هِيَ إِنَّ الْبَقَرَ تَشَابَهَ
عَلَيْنَا وَإِنَّا إِن شَاءَ اللَّهُ لَمُهْتَدُونَ / قَالَ إِنَّهُ
يَقُولُ إِنَّهَا بَقَرَةٌ لَّا ذَلُولٌ تُثِيرُ الْأَرْضَ وَلَا تَسْقِي
الْحَرْثَ مُسَلَّمَةٌ لَّا شِيَةَ فِيهَا ۚ قَالُوا الْآنَ جِئْتَ
بِالْحَقِّ ۚ فَذَبَحُوهَا وَمَا كَادُوا يَفْعَلُونَ
And remember Moses said to his people: "Allah commands that ye
sacrifice a heifer." They said: "Makest thou a laughing-stock of us?"
He said: "Allah save me from being an ignorant (fool)!" / They said:
"Beseech on our behalf Thy Lord to make plain to us what (heifer) it
is!" He said; "He says: The heifer should be neither too old nor too
young, but of middling age. Now do what ye are commanded!" / They
said: "Beseech on our behalf Thy Lord to make plain to us Her colour."
He said: "He says: A fawn-coloured heifer, pure and rich in tone, the
admiration of beholders!" / They said: "Beseech on our behalf Thy Lord
to make plain to us what she is: To us are all heifers alike: We wish
indeed for guidance, if Allah wills." / He said: "He says: A heifer
not trained to till the soil or water the fields; sound and without
blemish." They said: "Now hast thou brought the truth." Then they
offered her in sacrifice, but not with good-will [and it was close to refuse doing so for another excuse]. [2:67-71]
So you see, many of us are strayed and need such details of rules to remain on line! The holy prophet --peace be upon him and his family-- and his household --peace be upon them-- needed not such details. You can find witnesses for that e.g. in the Mi'raaj Hadeeth (حدیث المعراج) which states how the holy prophet learned to do the prayer (and now prayer is the mi'raaj of any believer: الصلوٰة معراج المؤمن); also you can read about the first Surah of Quran (Al-Hamd) how the holy prophet learned it (note the name Al-Hamd and the holy prophet's name Ahmad to better understand the situation); also you can read about how Imam Ali --peace be upon him-- learned a thousand of things in one night from the holy prophet --peace be upon him and his family-- from each of them he then learned a thousand of things further; also you can read about any previous prophet --peace be upon him-- how they were obeying Allah based on a very small amount of information (not a very detailed command) and particularly I grab your attention to the story of two sons of Adam --peace be upon him-- when they were each to present a sacrifice for Allah:
وَاتْلُ عَلَيْهِمْ نَبَأَ ابْنَيْ آدَمَ بِالْحَقِّ إِذْ قَرَّبَا
قُرْبَانًا فَتُقُبِّلَ مِنْ أَحَدِهِمَا وَلَمْ يُتَقَبَّلْ مِنَ
الْآخَرِ قَالَ لَأَقْتُلَنَّكَ قَالَ إِنَّمَا يَتَقَبَّلُ اللَّهُ مِنَ
Recite to them the truth of the story of the two sons of Adam. Behold!
they each presented a sacrifice (to Allah): It was accepted from one,
but not from the other. Said the latter: "Be sure I will slay thee."
"Surely," said the former, "Allah doth accept of the sacrifice of
those who are righteous. [5:27]
and read about the story how different were their sacrifices. Qabeel used his astray heart and embellished his desire for it to be admittable with a simple justification that "Allah needs not my sacrifice but I need my best stuff for myself" while Habeel used his healthy heart and did what was asked from him by God in the best way that he could, so his sacrifice was accepted and the rest of story. This is almost the same how all the men of God obey Allah through healthy hearts with good will and the best that they could without any justification and giving a chance for any wrong desire to affect their behavior. But anyway, they are they and we are we. We could be like them if our hearts were not sick. If Allah and obeying Him was our first concern, if the Hereafter was great to us and Dunya was less important to us. In another Hadeeth from the holy prophet --peace be upon him and his family-- "... دائکم الذنوب و دوائکم الإستغفار" which implies your disease is your wrong deeds and your cure is asking for forgiveness.
To conclude this answer, our hearts are sick due to our wrong deeds and intentions, but if we recover by asking for forgiveness and obeying Allah and His prophet --peace be upon him and his family--, detail by detail (so that we need the details now), then we would not need such details after the health recovery of our hearts, as the details would themselves be quite clear to us through our Fitrah. There is a very famous statement (at least to Shia Muslims) that clarifies this conclusion best: "کلما امر به الشرع امر به العقل و کلما امر به العقل امر به الشرع" which implies anything that Islam orders to also intellectual power will prescribe and anything that intellectual power orders to also Islam prescribes. And of course now you know that the intellectual power is based in heart and the statements to be true needs the heart to be healthy!
Hope you have gotten your answer. Godspeed.