Thanks for the suggestions, nrapallo.
The game disk itself says PS2 on it, so I'm pretty sure that it's a PS2 game. Also, the console hasn't ever given me trouble with the PS1 games I've used in it.
I've tried putting it in after removing another game disk that does work, and when I was polishing it all those times, I left the console on (for ... probably 40 minutes all told), so I assume
it ought to have had plenty of time to warm up under those circumstances.
I do appreciate the suggestions, though, thank you.
I didn't even know about the PS1 emulation mode, I'm glad to know of it regardless.
Does anybody know why the 40GB PS3 won't run PS2 games, but will run PS1 games? Or has that has been ... dealt with somehow by now?