Hi Mark,
you may well find the problem with the motor is caused by the bushes being seized in their housings, this is a common problem with C5s that have been standing around for a long time. If you look into the rear of the motor the bushes are visible. With care use a small screwdriver, or something similar, and see if you can ease the brushes back from the armature. If they don't move, or move but don't return then they are corroded. The other possibility is they are worn and there is insufficient pressure from the springs to make a good contact.
A couple of questions, how good is the condition of your battery, and do you have a multimeter?
As Marty commented, never push the C5 backwards quickly, this can only result in damage to the CB.