If the pick-ups were clogged, flush the tank, change the filter, clean the injectors & fuel rail. Check the fuel flow after it's buttoned back up. The fuel system must be clean enough to eat off of.
There's another problem that can cause this...bad crank angle sensor. Test it by checking resistance. Should be around 650 ohms, give or take 50. The cam sensor should be about twice that, 1280-ish.
These cars are famous for this fault...DME can't see a signal, kills the fuel pump relay...sets no codes. You can test the fuel pump by pulling the relay and jumping pins 87 & 30 IIRC. If the pump turns on when the key is in position II, it's most likely the crank sensor.
If you ever run into a later e36 M42 with the same trouble, check the DME for water damage. They tend to flood after heavy rain or power washes.