Problem is fixed.

You guys won't believe it. Such a rookie mistake (or oversight) that I'll put it up as a glaring reminder to not take the stupidly simple stuff for granted.

At the outset of this saga, I'd checked battery cables first thing. Grabbed the cables and gave 'em both a good rattle. Battery moved a little, but cables on the battery terminals did not. All cool, right?

Nah.

This evening, out of sheer desperation, I broke out the wrench and took the positive cable loose and picked it up off the terminal. When what to my wondering eyes should appear, but a goddamned piece of pine bark. Almost like someone had put it there. Never even occurred to me to pull that lead as it wasn't loose and I never take it off to work. I always pull the negative cable. There are also fresh, treated non-corrosion pads on both terminals.

Hooked the cable back up, opened the door and saw the "door open" light. Reinforced, I put the key in the hole and got a good, strong buzzer. Turned the key and she fired right up.

So, I cranked up the awesome audio and basked in the stench of the exhaust for a few minutes while dancing a little jig in the driveway.

Thanks very much to all who contributed. I was damned stumped.