1996 Nissan Maxima 1996 Nissan Maxima stalls and drains bat

I have a 1996 Nissan Maxima. For the last couple of months it has been stalling after a few minutes of driving in town. It usually stalls when in idle or when I try to accelerate from a stop. It has been re-starting but it has gotten worse. Now, the symptoms begin with the Air Bag light flashing and the radio losing power and i hear static. The rpm's start to sputter up and down and I have to floor the gas to go about 5 mph until i can get somewhere to park it. The engine dies as soon as i let off of the pedal. I just cleaned the mass air flow meter three days ago and replaced the battery. It seems that something is draining the battery. Any help is appreciated.