How do I fix my 2002 Chevy Malibu cassette player?

My 2002 Chevy Malibu is refusing to play tapes. I insert a tape, and the player makes a whirring, clicking noise as if it is attempting to play the tape. Then it spits it out after a few of these noises. I have tried to clean it with a cassette cleaner, thinking that may be the problem; however, it won't keep those cleaning tapes in there long enough to even execute that step. Any ideas on what could be wrong?

Sarah
February 2009