I think I may have the amp remote and ignition sensor wired into the wrong place. My old stereo never turned off when I turned off my ignition, so I think that wiring's been messed up for a while anyway. Is this a possible cause of my problem?

Yes, this could possibly be the cause of the problem.

If you are lucky, you didn't fry anything. If you are unlucky, you might need to send your player in for repair.