Lego Racer kit with Chargeable Cars
The set is 8364, and you can see it here: http://www.bricklink.com/catalogItem.asp?S=8364-1

The motor is part 5313a: (http://www.bricklink.com/catalogItem.asp?P=5313a)

Unfortunately, they do not seem to be widely available. The current inventory has one guy selling one as-is (untested) for $10 in the US, and one guy selling a working one for $40 in Israel. You can replace the whole set for a substantially higher price. Sorry I couldn't be of more help for replacing it, but hopefully now that you know the set and part numbers, you can search elsewhere.