Are you using MP3 Cd's , or maybe CR-RW (rewritables), or multisession cds ?
My elantra's cd player can play original cds or burned, but only Audio cds (the one that only stores 80 minutes of music, or 15 tracks average)
And if you are using burned cds, you should use CD-R kind. no CD-RW, no DVDs, and no multisession, etc.
Hope this help !!! =D