After discovering and replacing my dead PSU, I was able to boot back into Windows. Everything seems to be working fine, however, one hard drive is not. Windows 7 says that this SATA hard drive needs to be formatted before it can work. Can the data be recovered? Also, is there a way to check the integrity of the other components of my computer or assume they will work fine?
You should consider downloading the Ultimate Boot CD, a collection of 100+ utilities to run from CD on bootup that can evaluate your hardware. I routeinly use it to check memory (MemTest86+) as well as hard drives as they have manufacturer specific tools from Western Digital, Seagate, and others.
I'm fuzzy what other hardware it would help you evaluate, but its a very useful tool for someone in your situation.
try giving testdisk a shot on the drive