I have not one, but two dead 7-series cars with the same problem. The E23 733i and the E32 750iL both crank but don’t start, and their fuel pumps are quiet.  So, the pumps are either dead or not getting power.

My approach to isolating the problem is to check the fuses first: on the E23 it’s fuse number 11 and on the E32 it’s number 23 and 24.

If the fuse is blown, I should worry about the reason, but meanwhile a quick fix is to replace the fuse.

If the car still doesn’t buzz the fuel pump then … if there’s power at the fuse, then there’s probably also power at the fuel pump.  I’d then nevertheless go test that too …. a lot easier than replacing the fuel pump.  If there’s power at the fuel pump and it has a good ground, yet no buzzing then the pump is dead.

If there’s no power at the fuel pump, I’d run a hot wire to the fuse box to temporarily enable the fuel pump to see if the car will start.

On the E32 750iL it’s complicated. The fuel pumps are inside the tank and a lot harder to hear. And, there are two.  The odds of them both being dead at the same time are slim.  I happen to know that one of the two fuel pumps is already dead so maybe the other one now said “sayonara” too.