We had difficulty with an auto transport company who did nothing to move our car for an entire month.
They had promptly accepted a $200 deposit but were uncommunicative about the status of our transport. When they answered our voice messages at all, they seemed to be very evasive about what was going on.
A friend at work recommended UShip.com, where we hooked up with Apple Auto Transport. a week later, we had our car delivered without any hassle.