The fact that the blower starts after hitting a bump says a lot.
Put the car in park, start the engine and turn on the blower.
If you do not hear the blower going, then tap on the blower motor and see what happens.
If the blower starts, then you need to replace the blower motor (these are usually attached to the firewall behind the engine.
If the blower does not start, then find the blower relay switch and have it checked out.