I'm pretty sure I was wrong before.  I think the APU is working fine.  It may be the battery...which doesn't make sense since the APU should be providing power.

Anyway, when I flip on the battery and switch the DC meters to battery, the DC Amps meter has a positive indication.  When I start the APU and connect the APU generator, the battery DC Amps meter goes negative.

If I tune a VOR and leave the aircraft in that configuration for five or so minutes, I can observe the HSI shut off and that's it.  Everything else will appear to work normally.  All DC and AC meters will show power flowing for battery, stand by, and the APU.  The bleed air gauge will show pressure from the APU.  Everything looks fine (except for the HSI) until you attempt to start an engine and nothing happens.

I verified that the 727 is, as I would expect it to be, the opposite.  When you turn on the battery switch and set the DC meters to battery, the DC Amps meter shows a negative indication.  After starting the APU, closing the APU field and generator breakers, and closing the bus tie breakers, the DC Amps meter goes positive.

I also verified that I was wrong about ground power and air.  The DC Amps will show positive for battery, it will go negative after connecting ground power.  Wait a few minutes, and that's it.  I must have performed the pre-flight quickly when I thought ground power worked.