Yup - it was the ground!

Before reinstalling the 1 yr. old battery - which I mentioned didn't need a charge
1) I removed the ground and took a file to the head, which looked ever-so-oxidized.
2) I cleaned up the battery terminals as I did a year ago when I put this battery in the car.
3) I also wiped off most of the anti-seize compound I used when I removed the ground 6 or more years ago.

I think the slight corrosion was enough to cause this problem. Also, in hindsight, I can't help but think that the ground may be the only threaded item I shouldn't have used the anti-seize on. I use it, sparingly, on almost every threaded item - spark plugs, wheel bolts (which I'm told is fine - anti-seize=yes, white grease=no), misc. bolts.

Thanks all!