Yes, a dead power steering fan will definitely cause the ps pump to overheat and eventually fail...  Something simple as a pebble jamming the fan blade can cause the fuse to blow (happened to my MINI).  Make sure the fan blade turns freely by hand without any grinding sounds.

Let us know how you end up fixing this.

Ken

Ken,

thanks for the hint about the 100 amp fusible link, I want to make sure I exhaust the electrical possibilities before a start testing the pump itself.

I did find the 30 Amp fuse, and found a blown fuse for the PS pump cooling fan in the fuse box on the left drivers kick panel. I'm thinking the cooling fan not working may have contributed to the pump failing

RR

Tangent: I once replaced a bad power steering pump with a used one. It eventually went bad as well. But it kept working (still had functioning power steering) but what the car would NOT do was it would NOT shut off. Turns out the power steering pump was backfeeding ignition system and the whole car even when the key was turned off and the key was removed... it would stay running as if the key were never turned off. Only way it was found was by unplugging stuff until the car shut off.

Have you checked the fuses?

There is a 100 amp fusible link (FL4) in the engine compartment fuse box.  The fusible link is on the bottom side of the fuse box (you need to flip the fuse box over to see the fuse).

There is another 30 amp fuse (F08) on the top side of the same fuse box that protects the power steering pump, cooling fan, and the heater - AC blower.

Ken

Do you have any stored codes? the pump motor? is only part of the electric steering system. It all has to be happy or it won’t work. Plus the manufactures don’t want lawsuits and are usually a little pissy about sharing all the information on it. You may have fixed it, but it has to be flashed into the vehicles memory, it is a bmw after all 

Replaced failed electric power steering pump on my 04 S, but power steering pump still inoperative. Before I dive back down under the car, does anyone know if there are electrical issues I should check first. 
Maybe the pump I bought (rebuilt) is bad?
thanks