actually, the computer tells the fuel pump to run when it senses spark via the tach pulse if I'm not mistaken, however if your crank sensor is bad you get no spark.
I have had problems like this before (actually one of my e21s has one like this now). If you can jumper your fuel pump straight from the battery and just let it run while you get in and crank it, if you have spark it should fire. Don't worry about letting the pump run a while, the FPR will send any fuel over pressuer back to the tank.
If you have a timing light, hook it up to one of the plug wires and watch for a good strong regular pulse. That will let you know if you are getting spark. If it's erratic you know you have a problem.