It sounds like a bad cord, do you see lights or hear the timer motor? I belive I read that the solenoid is wired through the start windings of the motor, unless the motor is running at top speed, the solenoid won't energize. Your belt is a 4L420, available at most hardware stores (Ace, Tru-Value, Hardware Hank) for around $7 - don't pay $25 on Repair Clinic!
Should the need arise, use a 5/8" dowel pressed up against the rubber top of the agitator, then snap the cap back on. In machines where the agitator is stuck, you can remove the rubber diaphram, pack the agitator column with snow or crushed ice until it is cupped over the top; stretch the diaphram over it and snap on the cap. The ice will melt and the cap will return to it's normal position. See Jon, there is a use for that KA 'pelican-head' ice chipper after all!!