I think you might be dealing with negative pressure as you suspected. Here's what I'd try to figure it out:
First, open one of the safety valves on top of the hydraulic tank to let outside air flow in. You could also try using an air compressor to push compressed air into the tank.
Then check the suction port of the main pump itself. I ran into the same problem once, and after troubleshooting for days, I found a foreign object was blocking the suction port on the main pump. That turned out to be the issue.