Hey everyone, good news! Everything is fine now (as far as I can tell).
Thanks to everyone here!
I backed up everything I could on my spare 3TB drive. That went fine.
Then I read that updating the Intel Rapid Storage Technology drivers would fix my problem, and it sure seemed like it did! So I installed the latest version of Intel RST. Then, I ran chkdsk /r one more time and it looked like it recovered thousands upon thousands of orphan files and some other stuff. Results are below:
I tried a couple of the problem files I remember, and everything is working flawlessly. Doesn't seem like I had any bad sectors or anything like that. I suspect a few things. Like I said before, the power cable was loose at one point. Then, I also reinstalled Windows 7 so maybe I didn't update all the drivers and stuff for the 3TB storage, which has different requirements than the smaller drives. Also, at one point I was trying to recover some files from a mac drive for a friend, and the MacDrive software was extremely intrusive and probably caused some issues. i don't recommend using macdrive or any virtual mac drivers, they are awful. I've done it three times now and it has never been smooth. I'd avoid at all costs.