No, your usage of pirated version of Windows 10 is not halal.

As the Dr. Zakir Naik has put it in the linked video, piracy is haram and your case does not fall under the exceptional cases he has mentioned. Because,

1. It is not an established fact that Microsoft encourages pirating it's operating system.
2. As of this writing, anyone can use Windows 10 for free. It just will be in "not activated" state if one has not purchased a license or did not upgrade from a genuine version of Windows 7/8.
3. If you truly had a genuine version of Windows 7 and you have lost your key, you need to contact Microsoft to reclaim your original key. I am sure you can contact to their sales team through their website. Alternatively, you contact a local representative office. Microsoft has offices around the globe, almost in all countries.
4. If you do not really required to use Microsoft Windows, there are free alternative operating systems (Linux being the most popular one). You may for example, use FreeBSD, Fedora, centOS, Debian, Ubuntu, LinuxMint or openSUSE instead. There is even one that resembles macOS - elementary OS.

No, your usage of pirated version of Windows 10 is not halal.

As the Dr. Zakir Naik has put it in the linked video, piracy is haram and your case does not fall under the exceptional cases he has mentioned. Because,

1. It is not an established fact that Microsoft encourages pirating it's operating system.
2. As of this writing, anyone can use Windows 10 for free. It just will be in "not activated" state if one has not purchased a license or did not upgrade from a genuine version of Windows 7/8.
3. If you truly had a genuine version of Windows 7 and you have lost your key, you need to contact Microsoft to reclaim your original key. I am sure you can contact to their sales team through their website. Alternatively, you may contact a local representative office. Microsoft has offices around the globe, almost in all countries.
4. If you are not really required to use Microsoft Windows, there are free alternative operating systems (Linux being the most popular one). You may for example, use FreeBSD, Fedora, centOS, Debian, Ubuntu, LinuxMint or openSUSE instead. There is even one that resembles macOS - elementary OS.