LM324's are notorious for going bad.....for some strange reason especially on Centi boards.
The one on my board was kaputt too. I figured this out with the "wet finger" method

Seriously: I had no sound and was touching around the LM324 (which is an amplifier (OP-AMP) chip) and suddenly I started hearing some faint sound. Replaced it and sound back.
From what you write it's pretty clear the LM324 is toast and shows a full short (you could measure on the LM) between the inputs.
If that is true and the POKEY survives getting +5V on the sound output (pin 37) it would say the POKEY is a pretty rugged design, but I can sure imagine it's not going to like it

You say it's socketed, so maybe at one point in time it was put in backwards and failed like that because of this.
I have a quite a few of them if you need one or two, PM me your address if you don't have'm.