And especially your writer and MODEL. Mafia uses the SafeDisc 2 protection (v2.70.030) and you need a writer that can handle this protection. When playing from your writer make sure you have enabled 'Hide CDR Media' in the CloneCD tray. More information on Mafia here by PaRaDoX.
Eeh just read your thread more closely and I see the game won't even install. Have you tried installing from the original discs? Then make a back-up and use these discs to play with. Also try using some other media if you can. Lower your write speed perhaps?