Dead/Dying Fuel Pump?

I've been having some trouble lately with my 1988 Ford Mustang 2.3L (4cyl). It sat in storage for almost 15 years but was resurrected last summer. Since then however, the car has never started easily (i usually have to crank it 2 or 3 times while pumping the accelerator), it stalls sometimes, and when I drive it it will occasionally sputter while accelerating in any gear, and sometimes nothing happens at all. If I simply floor it, the sputtering usually goes away. I can hear a buzzing/electric spinning sound from the gas tank, so I'm suspicious that the fuel pump may be at fault, but I would like to be as sure as possible before buying a replacement. Any ideas or help would be appreciated.