See if the drive shows up in Apple System Profiler (in the utilities folder in apps folder, or click "more info" after opening "about this mac".
The drive should be listed if you click the "devices amd volumes" tab.
If the drive is listed, and its an LG drive, these fail alot. You will need to replace it (preferably with a different drive).
You can save money by buying a PC notebook DVD ROM (get a panasonic, matshita, IDM, toshiba etc) and fitting it to the caddy of your existing drive. This requires a small screwdriver, nothing more.