Dash lights w/ failed alternator?

[Robert Deis]

Patient is 86 5kTQw.

Driving home yesterday, the little voltmeter I have hooked up to the
cigarette lighter varied a lot between 11.0 and 12.5 or so volts. This
seemed to correlate with the load on the system (i.e. whether the radiator
fan was on, etc) but its hard to tell for sure.

Then without warning, the voltage began to steadily drop until it was so
low the sensors were giving confused readings and the car barely ran.  I
coasted into an auto parts store and they charged the battery for me and
sold me a new alternator.

The charge in the battery got me another 6-7 miles (to my in-law's house)
Voltage dropped from 12.8 to 10.1 along the way.

I swapped the alternator there and drove the 70 miles home. Voltage varied
between 12.8 and 12.0 along the way home, but the dash lights wouldn't
work.

Went to start it this morning and the battery was dead- 2.5 volts at the
posts.

Jump started it with a good battery, and everything seemed fine- dash
lights were working, too, and I measured 13V at the posts, and maybe 14 at
the alternator (crummy voltmeter..)

Shut it off, waited for a little while, and the dash lights stopped
working again- any battery voltage dropped to 2.5 again.

What's going on here?  Can you tell me where to start?

--
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  Rob Deis                  "Let the people know beforehand what the law
  MiB3347                      is and what they are to expect."
  rdeis at io.com                              -- 18th Congress, Rec. 75