blower motor will not work when car is running.put key in on position blower works

The blower motor circuit requires a lot of electrical current, so when the key is just on, it has sufficient current, however when the engine is running, there is no longer enough current to operate the blower motor. First verify that the blower motor has a very good ground. Then I would test the blower motor fuse for power in both states to see how much power is being lost, then using a wiring diagram, you must trace all the all the 'legs' of the power feeds involved with the blower motor circuit to pinpoint which power feed is weak with the engine running and why.