Some really good responses from many of you. Thank you very much.
I'll check the trim pots and woofer terminal connections and see where we are from there.
I just got these 4312s a week and a half ago. Cosmetically, they are in VG+ condition. I'm really hoping that this is just something minor and not something that I'm going to have to put a lot of major coin into repairing. If so, I guess my decent deal wasn't so decent, afterall. But I'll just remain optimistic for now and hope it's something relatively minor.
Will report back with my findings. Thanks again.