I had a similar problem where I thought my MistKing died.
Turn on the pump and put your hand on the pump enclosure. Does it hum? It may be so quiet that you can't hear it.
If the pump is humming, then everything is working, it just needs to be primed. As described above, detach the tubes from the mister nozzles and run the pump for a minute or two to clear the air from the lines.
If that doesn't work, get in touch with Marty at MistKing directly, and he can definitely help you. His customer service is tops.