Gas also lubricates the pump rotors as well as cools it, so running a pump without the gas will burn up the pump. Gasoline is just very lightweight oil.
Don't rule out the PCM control of the Fuel Pump. The controls on the fuel pump are designed to prevent the electric pump from spraying gas everywhere after an accident.
*The pump will not run if there is no engine rpm, the PCM cuts off the fuel pump if it sense no engine rpm. To start the motor (since there is no RPM at first) the PCM will activate the fuel pump for 2 secounds right after turning the key on to build fuel pressure up in the system, but shut it off until the PCM senses engine RPM.
*Roll over valves and vents, there are controls on the fuel pump and gas tank to prevent fuel from spilling all over if the vehicle rolls over, there are vents and lines on the top of the tank for this. I'm not sure how the system works, but its possible that a bone dry tank could trigger something to kill the fuel pump, thinking its a roll over tank.
*Trapped fuel, the pump runs dry with a little bit of gas still in the tank, slosh, gap between the pick-up and the bottom of the tank, etc. When I changed out a fuel pump in my mini-van, I had to drop the tank, which I drained bone dry. It took 4 gallons of fuel poured in the tank before I got the motor to start, so your 1/4 of gallon is probably nowhere near whats needed to get gas pumping again.
*Noise, the pump probably makes a very different noise pumping air and gasoline. So just because you hear no noise, doesn't mean the pump is not working.
I'd check these all out before I spent a lot of money on a new fuel pump, it could be possible your pump is fine.
Get a voltmeter and check voltage at the plug from the car, if there is no voltage coming from the car, than most likely its one of those safety features above that is purposededly cutting off the fuel pump. If you do have voltage and you have 5 gallons or more of gas in the tank, but no fuel flow with the motor cranking, then I would suspect a bad fuel pump.