To make a long story short, I managed to have to wipe my entire hard drive. Fortunately, I have a Time Machine backup ready to work. Unfortunately, I can't find any way to get the option of restoring it.
I have the Snow Leopard DVD somewhere in the house, but after somebody moved it, I've completely lost track of where it is. I've ransacked the house and found every other disc I've ever owned but that one. If I could use it, I would have by now, and I wouldn't be here asking this question.
I do have some resources. I have a copy of the "Install El Capitan" program with its .dmgs sitting on the other computer's hard drive. The trouble is that that computer has Snow Leopard, and that's the last version of OS X that it can run. That's a problem, because Snow Leopard doesn't have access to createinstallmedia, which I understand is the go-to solution for this kind of thing.
I followed the instructions in this question, and it got me as far as making a bootable USB flash drive that has El Capitan on it. The trouble is that it can't install it (it gives me some "undefined error 0" or somesuch), and for some reason, the menu that usually allows you to access Time Machine recovery is nowhere that I can see, even though the installer suggests that it should be available.
I got cute and tried to access it through the Terminal, but apparently recovery/installer-partition Terminal is crippleware, as it doesn't come with the "open" command.
I've spent most of my waking hours since 4 AM this morning stressing about this, and it'd be nice if there was a relatively easy, viable solution that I'm missing. If not, I do think I know how I can fix it (create another boot drive based on the Snow Leopard Mac with Carbon Copy Cloner, then copy the installer onto it and run it from the flash drive), but it'll take hours and I'd like there to be a quicker way.
Thanks for any help y'all can provide.