My 1984 BMW 633 CSi (with the M30 engine) refused to start one day. Over the most recent few weeks, the fuel pump had become progressively louder, and that had been my cue, but I’d chosen to ignore it. Finally, something broke.
Had I not suspected the fuel system, I would first have tried to start the engine on starting fluid, and if it started then, I would have concluded that the fuel system was the problem. But, I had my suspicions as to the latter already.
I like to split fuel system problems into fuel supply vs. everything else. To test the fuel supply, I pulled the hose off the fuel rail, towards the back of the engine compartment. I made sure there was plenty of fuel in the tank, and then I used the key to crank the engine. No fuel came out the hose. That told me the problem was with the fuel supply.