Yes, sounds like your tank has a vacuum right now. Opening a faucet will not help, because the air has to somehow flow from the faucet, back through your water pump and then into the tank. The pump is sealed, air will not flow backwards. Good idea, wrong method.
Disconnect the in-take water line on your water pump. THAT will break the vacuum, and probably break free the vacuum in your pump as well. It's quite obvious the pump is stuck (with pressure on it).
That will help you drain the tank, but something caused the vacuum in the first place. Your vent to the fresh water tank is closed up, stuck, or something stuck in it not allowing it to vent. That's probably the real problem.