Windows 7 restarts after loading screen.
This is the only piece of information you gave that is actually related to your problem. Based on that, you have one out of several hundred or thousand possible problems, but it's affecting startup.
Given the limited information, there's not a lot to go on other than to suggest that you run a Windows 7 Startup Repair. This can be run from either a Windows 7 Installation Disk, or by holding F8 on your keyboard when you start the computer.
If Startup Repair does not fix the issue, it is in your best interest and time constraints to reinstall Windows. Determining the problem and fixing it will likely take longer than reinstalling.
The only other thing I would try is getting into a command prompt from the Recovery menu and run
bootrec /fixmbr, and/or
bootrec /rebuildbcd. Any one of these commands might be able to locate and fix the issue.
Power failure is not in the least bit predictable. If a blackout or brownout corrupted my computer, the first thing I would do is try to back up any needed documents from the drive and reinstall. I would not waste the possible days or even weeks trying to determine what that electrical anomaly did to Windows.
Is there any hack with which I could fix the Windows 7 installation using the Windows 8 I have in working condition?
There are certainly ways that you could fix some of the hundreds, possibly thousands of possible problems with one Windows installation from another, but unless you know exactly what is wrong (you don't, and we don't either), it would take just as long to reinstall Windows again.