Put direct power to the AirDog via the wires right at the pump or by jumping the red and Yellow wires in the relay. This will bypass everything else and tell you if the pump is working or not.
If you put direct power to it and it doesn't run then it more than likely if a pump issue.
FWIW: My pump went out on me once 2 yrs ago and when it did the truck wouldn't run. However, since then i've run the truck w/o the pump turned on no problem. Not sure what it is but some trucks can pull through them and some can't. Has nothing to do with the pumps though.