Thanks for the tips!
I already know that I have to replace the radiator, since the metal fins are all blown out and corroded along the bottom of it. It looks like I might have more than one cooling system problem--like maybe a bad thermostat and and bad fan clutch, since the fan doesn't go on at all.
My bigger concern is whether any engine damage was done while my friend drove this car without a cooling system. He said he only drive it twice after it started going hot on the dash gauge, but one of those times was a 40-minute trip, and just as he reached his destination, the engine shut down automatically. I'm not sure what that means. Does toyota have some kind of an auto shutoff device for when engine temps get dangerously high?
When I idled the car last night, there was no white exhaust, no milky oil, and the idle was fairly smooth, but low. Besides checking the compression, is there anything else I can do myself to discover any possible engine damage? Should I take it into a shop, or just assume it's OK as long as it's not spewing white smoke? Thanks again.