Download a program called CDCHECK click here put you corupted CD in the drive and run the program in 'Recover' mode.
This will attempt to recover the CD onto a folder on your harddrive, from where you can create a new CD.
It may be the the CD is sticky or dusty, which is why it is not playing.
Put a small amount of Flash liquid (or similar) on a soft cotton cloth, and wipe the CD in a circular motion, starting from the centre and moving out.
Allow to dry (a few minutes and try again.