What are the rulings on paying taxes to governments that are corrupt? You know well that the money you give doesn't go to the government system, gets lost in the way and probably finds its way into the pockets of corrupt government officials.
Being a citizen of a country, it is your obligation to follow the "law of the land". If you have proof of some corruption, the right way is to take it to court or to the people who can take the corrupt people to task, within the laws. If you think that it is not possible, than its better to leave the country. What you can not do is to fight a wrong thing (corruption) with another bad thing (breaking the law)
I can well understand the situation as described by you. As @goto suggested, one option is migrating to another country. Though this may not be possible overnight -- uprooting one's family and re-settling elsewhere is not a decision to be taken lightly -- I would strongly recommend that you consider this option.
About the matter of taxation:
One option that could be recommended is to "go by the book," that is obey the law in word, as precisely stated in the books of law. Never ever do anything that could potentially be deemed illegal going by the definitions of the law of the land. Tax evasion is a punishable offence in most such countries, so be wary. For example, many folks try to avoid or reduce taxation by not recording some cash transactions in their. Rather, try to find ways to legally minimize your tax liability. An experienced financial consultant is invaluable in this regard.
About the money not getting used for the right purposes, I would say that you keep this Quranic warning in mind:
So you can be sure Allah will call to account those who took your money for supposed public good and did not utilize it in the correct way. And even an atom's weight of money will be accounted for and the Muslim will be (more than) compensated. And remember that a Muslim is never in loss.
About the matter of corruption:
In theory, corrupt officials can be brought to book but typically the laws are so convoluted that it would take years or even decades before they are even proved guilty of corruption, leave alone the matter of actual conviction. So that's one course of action that may not be practical. In theory everything is possible, but most people are looking for practical solutions to their problems.
One thing I have realized is that when corruption is widespread in a particular society, where corrupt officials use the law to extract money from law-abiding citizens, avoiding corruption is nearly impossible if you need to get any work done. For example, at some point you will definitely need to interact with some officials who are invariably corrupt and will withhold even your basic rights from you (for example, issuing licenses) if you refuse to pay them "under the table."
I really do not know what advice I can give to you in this context. Someone may suggest that you always do what is right (so avoid giving corruption), which is a politically correct answer to give, especially if the adviser is fortunate enough to live in a nation where corruption either does not exist or is minimal.
Sometimes though, life throws a situation at you where the decision boils down to a choice between the lesser of two evils, especially when the two options are: a) give corruption; or b) lose your means of livelihood.
In this case, I would recommend that you give this question due consideration and do whatever your feel is right in such a situation. From my understanding of the Sunnah of Allah, I feel that He will judge each of us uniquely according to our situation. (And none can coerce Allah and His Will is absolute.)
Finally, I would strongly recommend that you consider migrating to another land where you can avoid these problems.