Thanks for the quick and good response, aqua!
Man, we're lucky if any starter batteries last 2 years here in Phoenix. But, that's part of the puzzle - this battery is brand-spankin'-new! (Put in car by AAA 2 weeks ago, manufactured in May 2010.)
Another piece of the puzzle - the starter battery was put in the day after a "new" IMA battery pack was put in (at the dealership). The car wouldn't turn over THE NEXT DAY!
(It has required a couple of jumps since then.)
More pieces: the IMA light, the ABS light, and the "brake" light have all come on at various times in the last couple of weeks.
Dealership got an 81-01 code (ABS, sensor) off it today, but couldn't get any other codes. They also couldn't get any of the lights to come on this a.m. - I'm thinking it is only after the car has sat for several hours.
The dealership first recommended (said that Honda's tech line recommended, actually) the ABS pump modulator. After I had a long discussion with them, they took it out again, did some more research, and concluded that it is the starter battery. (Your conclusion, too, aqua!)
The battery is still under free replacement warranty, but AAA is going to fight replacing it (again) and it is going to test fine. I'm debating whether to buy a different battery and do some comparing.
BTW, it is a '04 HCH, with 151,000.
Thanks again!!! (any other opinions welcome, too)