How to fix a portable DVD player?

I have a cheap portable DVD player that isn't worth having fixed professionally but maybe it's something I could do myself. It's an Insignia, and it all of a sudden stopped recognizing when a DVD is put into it - it runs for a while then says "no disk." I've tried using a CD-cleaning disk which didn't help. Is there anything else I could try? I'm not that worried about wrecking it, since it's pretty much just a paperweight at this point anyway, but I'd be pretty happy if it would work.