No oil pressure can cause a no start, GMH 3.8 v6's (buick to you US lot!) use a 3 pin oil pressure switch which causes the ecu to cut the fuel pump in a no oil pressure situation or 5 seconds after a start if the oil pressure doesn't come up. I don't know if BMW ever used them on the older models but they do on the E60's.
BMW parts professional
Previous rides:
BMW
E12 M535i (go the dogleg!)
E28 M535i (MMM M88!)
E34 535i M
MAZDA:
RX7 S-IV T04 (440 hp ATW)
RX7 S-I 13b bridge port
RX4 13b peripheral port