There are a number of reasons for a disc not to spin:
1) The loading of the disc is not complete - There is a small belt that controls the loading of the disc. If this belt slips, the loading process will not complete and the disc won't be read.
2) The laser is dirty or weak - In this case, you MAY hear the disc spin. If so, then the laser has detected the disc and is attempting to read TOC (table of contents) from the first track. If the read fails, the disc won't continue to spin. If the laser has completely failed, the disc won't spin because the system won't realize that there is a disc present.
The first thing to try is to open up the unit to gain access to the laser and GENTLY clean the lens using a cotton swab and alcohol.
Try that and update this with the results.
Dan