Water in fresh water tank ...check
Water panel 'FILL' valve fully closed...check (if open pump will just pump water from fresh water tank and back to fresh water tank ---Round Robin)
Turn pump on.......open faucet hotside and let water heater fill up and ALL air expel from line/faucet
Then do cold side
May take awhile for pump to prime....so let it run with faucet open
(Also check that pump suction side doesn't have an open winterizing valve or any air leaks)
And YES there are check valves in system
One is internal in pump.....prevents backflow thru pump when using 'city water'
One is internal in city water connection .....prevents backflow out city water connection when using pump