A key table in the database was corrupted, hence the earlier errors. Then it got progressively worse until the whole thing crashed. I believe I've been able to repair the damage, and everything seems to be golden again.
My best guess is that when the hardware failed earlier today, it hosed that specific table, and then sort of went downhill from there for the rest of the afternoon and evening.
Everything checks out now though, and I'm cautiously optimistic that we should see no more errors.
At least until the unknown hardware problem causes another crash, but at least now I know what to do after to check the tables.
Sorry all.