Car keeps dying while driving

[wateriswise]

Ok I've had a 1987 Supra Turbo for the last 6 months or so and its been an awesome car. But one day, I went out to start it and it was completely dead. I tried to jump it from my dads car and I got nothing. I connected the battery to a machine which connects to a 110 volt plug in my house so that I could charge the battery that way. I let that charge for several hours, took it off and I could start it just fine. I drove it to school the next day and right when I was pulling into my parking space, and let off the gas, it just died and I couldn't start it. It wasn't turning over or anything; just completely dead. I had it towed back to my house and I was told that it was probably just a bad alternator. I bought a remanufactured one and installed it, I charged the battery via 110 volt plug on the dead battery again, and I was able to start it and it was idling fine and everything. I drive about a mile, and it does the same thing, I feel the power steering about to go out so I pull over and it dies. I then had to have it towed home again. I have no idea what could be wrong with it. The battery is holding a charge fine so I don't think thats the problem, I know its not the alternator since its doing the same thing as the old one did.
Any Ideas??