Ok, time for an update.

Per the discussion here prior, I tried resoldering all the connections
on my IPC.  Actually, I resoldered everything, but only on the circuit
board that didn't have the VFDs on it.

Still no change, but here's where it gets weirder, and makes me think
that the IPC is not my problem...

1) I've tried an IPC from both a 1986 and a 1989 Toronado.  Both of
them were 'working' pulls.  Especially the 1986 one--it was in my
other Toronado and I never had *any* IPC problems with it.  Both units
lit up, and the 1989 one complained of an 'electrical problem',
understandably so due to the year difference.  Anyway, both of them
worked initially, but when I tried them later after my original IPC
started failing more often, they both are dead too.

2) I was trying to isolate the connection between why my climate
control switches to '- - -' when the IPC goes black.  In doing so,
I've waited for the IPC to fail, then I shut off the car and pulled
the IPC entirely and started the car.  The display still read '- -
-'...so I am making the minorly-educated assumption that the IPC and
CC are being driven by a separate device that is failing...the BCM
perhaps?  Note: I've also pulled just the CC to see if it was shorting
and causing the problem with the IPC.  No effect.

3) My interior lights.  When the IPC and CC are functional, I can
slide the interior dimmer switch all the way up and the interior
lights all come on.  When the system is spazzed out (IPC and CC are
failing), this does not work, and no interior lights come on when I
slide it all the way up.  I have pulled the glove box and the relay
that is triggered by the switch is fine.

My thoughts: The BCM is failing.  I looked at the schematics for this
car, and all of the failing systems: the IPC, the CC, and the interior
light dimmer control run *THROUGH* the BCM (Body Control Module).
Other things that still function, such as turn signals, exterior
lights, seat adjustments, door locks, window adjustments, rely on
direct hardware and don't seem to be as dependant on the BCM.

So, my question now is: does my hypothesis seem valid?  Has anyone had
similar experience?  My worry is that I've tried three IPCs here, and
two of them should have worked fine.  BUT, when the system is spazzed,
none of them come up.  I can't just assume they are all flaky.

Do I have a valid idea in blaming the BCM and wanting to replace it,
or is there a glitch in my theory?

Thanks in advance!!  I really appreciate all the help!