While waiting on hold with AT&T with
Wily,
Elementary started working on the old iMac! It's not garbage now!
Unfortunately, I don't know exactly what fixed it. Those ringing sounds were actually from the functioning Elementary OS. When I timed holding shift down during a reboot correctly, I was able to get to the boot loader, then go into recovery mode. There, I ran a repair of missing packages, then rebooted again, and everything worked.
My best guess is that wifi was lost during the initial install, and graphics drivers weren't installed, hence the blank screens.
So, that big pile glass and aluminum is usable now and doesn't have to be chucked for the crime of being ten years old.