Before you start, you should wait in key position 2 for a few seconds, just so the fuel system and electrical system can charge, then turn it over.
There should be a slight buzzing/humming noise when you leave the system to charge for about 3 seconds before starting. If this buzz/hum is not there, you're looking at either fuel pump relay or the fuel pump itself.
Check the relay first because it's easier to check. Try the good old fashioned "reseat" method. It is in the "E-box", the box on the other side of the engine bay and looks exactly like the fuse box on the drivers (left hand) side.
Fuel pump relay is the only orange one in that box:
If this doesn't change, the fuel pump replacement is found at Johan and Sean's E32 Page. The write up is for a 750 but I think the procedure is pretty much the same. Where ever there are two send lines, there will only be one for your car. If I remember correctly, he even touches on how to test them, if you feel like your up to it...
Fuel Pump Replacement
If there is a humming and the system is charging, make sure that your gear stick is in P. It might also be your starter relay, which can be found here:
http://bmwe32.masscom.net/johan/e_box/fuse_box.html
Let us know how it goes.