Possible fix: If the APU GCU or the Starter Generator are no help, APU remote fire switch (S16) located in the Rt main wheel well.
Tip: The contacts for the APU generator on the S16 are 1 and 2.
Reason: The S16 has a few different set of contacts, so it is possible for the set going to the APU GCU to be open not allowing the APU to be put on line, but the other set to be closed so the APU will still run. Reference: SSM 24-22-31, 26-21-11, 49-62-01, WDM 24-22-31.
Thanks to Tom S. for his input !