My one has a clunk from the pump until i open the flow valve, then it fires up................but it also won't fire up if the connection from backpack to hose is not secure (tight). I have an autostop hozelock connector which will sometimes stick and the pump won't run, as water can't flow. Soon as I give the valve a prod in the connector and connect it back up, its fine. Its probs not your problem, but its best to try all options.
Why not just run a 12v direct to the pump to eliminate any battery probs ??
If it still don't run, could be the pressure switch ??