1989 Oldsmobile Cutlass Engine stalling problem

Sometimes it will run like a top, but after dying when I put a load on the motor it fails to start. When it does try to start, it cranks, it fires, and it dies, all in a matter of 2 seconds. After sitting for an hour or so, it will fire right back up. This is a notorious issue with these cars. Today I started it and it started fine, so I got on the highway and accelerated, and when it hit about 45 it died, just like someone turned off the key. After that, it did the crank, fire and die thing for about an hour until I could limp back home, only to have it die in the driveway. After putting it in park, I revved the motor a few times and it ran like a new car. However, after putting it back into drive, it made it about 30-40 feet before the motor just cut off again. Once again, It did the crank, fire, die thing again. I've researched this online and could it be a bad battery? The car test drove great with a different battery, and I'm wondering if maybe the battery is refusing volts and spiking the ECM, killing the car. If this isn't possible, fill me in on your other theories. I really don't know what to do with this one.