undo a few bolts on the upper black plastic cover for the injection pump belt, pull it back a bit and look in. The cover is #6 here:
http://www.realoem.com/bmw/showparts.do?model=2583&mospid=47141&btnr=11_2367&hg=11&fg=10
Can you see the white Gilmer belt (#1 below), or do you see the teeth of the injector pump sprocket (#4 below)?
http://www.realoem.com/bmw/showparts.do?model=2583&mospid=47141&btnr=13_0682&hg=13&fg=15
If it is the latter, the belt broke. Inexpensive part, a bit of work but not too hard to replace. When the belt breaks the cold start solenoid gives a shot of gas to allow it to start, but dies immediately as there is no high pressure fuel from the injection pump.
Other than that, there is no reason to suspect the injection pump itself. Perhaps a linkage broke, check all of those to make sure the injector pump lever moves when the gas pedal is pressed. The fact that it died suddenly indicates something broke, or came loose and is out of adjustment (timing?).
They say 90% of fuel issues are electrical, so just because things seem to check out, go back over everything twice.
Fred (Broke a Gilmer belt on Hwy 17 in Santa Cruz my '73tii back in about 1987-88. Got it fixed at Catalpa Street Garage. Other than that, over 330,000 miles and a few hundred track days on the KF pump, never rebuilt.)
FB73tii's post in 1972 Tii Crankshaft And Camshaft Resistance was marked as the answer