Well, it turns out (after a lot of searching on the Indy's part) that the battery was leaking and corroded a wire that ran from the battery to the computer thereby causing the problem. 1 new battery and 2 hours of labor and $292.00 later. . . They only charged me one hour of labor until they found the problem then another to install the battery (doesn't seem like it should take THAT long). I was also advised that the battery that they replaced was "too small" for the car.

Thanks for all of your suggestions. . .

Anyway, she starts.

There are two battery sizes that will fit and both are listed on the
replacement charts. The larger one has more cold cranking capacity.
I guess your mechanic is in the size matters camp. Either should
work with the larger one a bit better if you live in an extremely
cold climate or have an after-market mega watt stereo system.

Corroded wires around the battery tray are not uncommon. But
typically it is the ground wire that I have seen reported (here)
with the corrosion problem.

What variety battery did they put in?

Interstate, I believe. . .

Been using Interstate exclusively forever and never unsatisfied with one of their products.

That's good to know. . . Thanks for the confirmation. Hopefully I won't have to have her in the shop for a while. . .

My 89 Dodge Raider no kidding went from Phoenix, AZ all the way to Tacoma. Then to LA (state), then to TX, then to Wisconsin, then to Alaska. Winter, summer, wet, dry, fog, salt... kept going.

I put it in in... oh... I think it was 89. Something wrong with the original and couldn't get to a dealer. It was in there in 97 when I sold it. Considering I did short trips at -50... anyhow - they're good stuff.