I had a similar problem with a Pioneer CD player and it was caused by dust on the rollers that eject the disc.
Easy way to get it out is to slip something that won't scratch the top of the disc (like a zip tie) into the CD slot above the disc. Give it a slight twist to apply some friction against the rollers and press the eject button again. This has worked for me many times out here in the oilfield where dust is quite a problem.
After you get it out you should get one of those dust remover aerosol cans (found in the computer section of Wal-Mart) and blast the crap out of the CD slot.
You'll be amazed with how much dust can accumulate in there.