Arcturus;
Failure to pump during testing, may be due to it not being primed, or Valves being installed wrong-way-round, or you having the Outlet submerged, thinking it is the Inlet. Clear your mind, and have another fresh look at it, presuming nothing from before!
I have also marked up your pic for flow, the way I expect it (if you first confirm the dotted connections I show).
Pump Function has two steps...starting with a relaxed diaphragm..I believe I have this right...
1. Inlet Draw: Actuating Lever is moved, diaphragm deflects, inlet draws IN fluid passed open Inlet Valve, in response to partial Vacuum created in internal volume (Outlet Valve is closed, since it only allows flow OUT, and none back in from output line, but also allowing no flow out at this time!).
2. Outlet Push: AL is released, diaphragm relaxes, and makes over-pressure in the Int Vol, and since Inlet Valve is now closed, fluid is pushed OUT passed Outlet Valve (Inlet Valve is now closed, since it only allows flow IN, allowing no flow back toward Tank).
In this way, flow in only the correct direction is possible also irrespective of AL (verifiable by blowing into the Inlet).
Hope this helps!