Before jumping to fuel pump..
On the drivers side of the engine bay, remove the black cover over the three relays. The white relay (should be the one toward the front) is the main relay. Does the relay click when you try to start the car? If yes, does the fuel pump relay right next to it click as well? If yes, then move on to test if you're getting fuel and spark.
Blah blah blah.. If you really want to find out, use the wiring diagram to trace it.
Follow the link.
Like the other guys mentioned, try the fuel pump
relay first. This one's really easy, as you can temporarily swap in any of the other 4 prong relays to test. I believe there is an o2 sensor relay right next to the main and fuel pump relays. On my very first e30, this was one of the first issues I experienced. You can also hear/feel the relay "click" (energize) when trying to crank the car. If there's no click, the relay is bad. It's not a bad idea to check / replace the main relay as well. The main relay is the 5 prong relay in the bank of 3 relays on the drivers side strut tower, by the fuse box.