My heater only works while the car is moving

I would check the fuse for the blower motor (may be bundled under "HVAC" or something similar, I don't remember for sure how it's labeled in the fuse box); if it's fine, check the blower's wiring for a short. It that's all good, I'd say the blower may just be dead; try replacing it, and that "should" solve your problem.