Sounds like it won't even let you stick a CD in? If that's true then the CD player is screwed, I sold my old stock radio to a lady and she said it wouldn't take a CD after she received it, she'd had the same problem with another CD player she received.
She sent mine back and I got the same results. She said that with the previous non-functional CD player, she had gone to a dealership and searched for hours to no avail. The dealership said it had something to with the CD player being shaken or dropped and something was either misaligned, or there is a piece that falls in place blocking the disc slot (can't remember which it was).
In other words, I don't think there's a fix.