Your symptoms normally would lean towards the bladder tank being shot (broken or leaking bladder), but when that happens, the tank ends up totally full of water, when there should be figuratively a big balloon of air in there, with water filling the rest. Are you sure the tank is empty?
The pressure gauge would normally show the turn-off pressure, but if there is no air in the tank, any small leak will cause the pressure to drop quite rapidly since water doesn't compress (only a little loss of water would drop the pressure and cause the pump to turn back on).
If you turn off the pump, open a faucet and watch how much water comes out. That is the stored water from your tank which is being pushed out by the bladder under pressure. If you don't get any water out under pressure, there is a problem.
Now that you have the pressure off of the water, take a tire pressure gauge and check the pressure on the air valve at the (usually) top of the tank. Depending on the switch for your pump, (30/50, 40/60, are examples), the air pressure in the tank should be 2# less than the lower number. My guess is it is low, which means it doesn't have the ability to store much water under pressure.
If you get water out when you check the pressure, then the tank is shot and needs to be replaced. If you don't, and you have a bicycle tire pump, pump it up to the needed value. If it holds, then close the faucet, turn on the pump and see if that resolves the problem.