Hi Mike,
Great, if the drive shows up in My Computer, then it's very very likely to be a hardware as apposed to a driver issue. Either the heads of the drive are dirty or worn. If they are dirty, then it's just a simple matter of using a cleaning CD. If the heads are worn or damaged, then your best bet is to replace the DVD drive completely.
You can purchase CD lens cleaning kits from many supermarkets and hardware stores. You can also purchase them on-line, for example:
Read Right RR257: CD ROM Lens Cleaner | OfficeWorld.com