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.