After blowing like eight hours trying to get my Mac to work, it finally started working randomly after a reboot.
I tried booting from the OS disk to restore from the Time Machine backups. That is what the backups are for, after all. Unless, after booting from the OS disk, the spinning beach ball of doom appears on the “Choose the backup drive” screen. At least I know I have to figure out what is wrong with the Time Machine backup system…
Repairing the permissions may have helped, but who knows? I’ve rebooted several times and each time the Mac has come up just like it should.
I’m just glad to have the system back. I’m using a secondary drive to mirror my primary drive so I’ll always have two bootable copies of the main drive and my data.