I think you need a new tank. Replacing it shouldn't be too bad. If you turn the pump power off and open a faucet somewhere, you'll get most of the water out of the tank, enough anyway so that you can move it after disconnecting and not have a flood.
The tank will likely need the air pressure adjusted. Think of it like a big ballon - there is a valve just like the one to fill your tire up on the tank. You check and adjust the air in the same manner. You want 2 pounds LESS than the pressure when the pump turns on in it when there is no water stored in the tank. Hook everything back up like you have it, and it should work once you apply power.