If you can hear the fuel pump spin up for a second after you turn the key to the on position, the next suspect would be the crank position sensor. I don’t know where they put it on the e46, but on the previous model it was on the front of the engine near the air conditioning compressor, as I recall. Access from beneath. Tough to get hold of, very tight clearances in there. If you can get to its lead, unplug it and make sure it is not corroded. That is a very weak signal, so a tiny bit of corrosion will stop you.