Yes, it is possible sometimes to repair a microwave. Some problems can be repaired economically if you can and are willing to do the work yourself, and a non-turning turntable could be one of them.
It is unlikely to be economical to pay someone to repair the microwave, however.
You absolutely should NOT try to repair the microwave yourself unless you know and understand the very real electrical dangers involved. The power supply for the magnetron is easily capable of killing; it produces a few thousand volts at a substantial fraction of an ampere, a good recipe for electrocution if something goes wrong. As was mentioned, the capacitor in the circuit can hold a substantial charge even after the oven is powered off and unplugged.
There are some good sources of information on microwave oven repair on the web.
This FAQ by Sam Goldwasser is one of the better ones.
Before diving in, double check to make sure that the turntable spinner doohicky is properly seated on its shaft and the little wheeled ring thingy is in the right position and everything is otherwise correctly lined up and installed.