Weighing in here to say this is a perfect example of problem solving on Avsim. I had this issue, read the posts this morning but there was no resolution, re-loaded the page this evening, problem solved :-)

You can see the APU exhaust opening at the tail of the aircraft if the APU is running

Not had an issue with this doing Cold ' Darks. I just turned on the BATT, then the APU, and yes, verified by seeing that exhaust opening, waited for less than 3-4 minutes, and then the MCDU nomenclature lit up faintly, at first, giving me access to turn on the Ground Services. After that it was plain sailing.

Thank you, this helped me as well!

I was able to reproduce the issue:

 

This happens when you load the cold an dark state right after a previous state, in which the apu was still running/not finished cooling down.

 

When shutting down the apu in the default state (+ cool down time) and THEN loading cold and dark it finally works.

 

Hence my stuck apu rpm value in my previous post.

 

This is bug that has been already identified and fixed for the next update.

As you mentioned it happened when starting up fsx with a panel state in which APU is running (like the default SHORT state), then switching to a cold and dark panel state and try to start again the APU.