First off, unlike Battery Recondition for NiCds, Battery Reset does not (nearly) zero out the charge in a lithium ion battery (fully discharging a lithium batt is a Very Bad Thing, as it turns out). Although lithium ion cells are free from the "memory" effect of NiCds, they do suffer from a form of digital memory problem if they are not regularly allowed to cycle fully. Basically, as the battery ages, the correlation between cell voltage (with and without load) and remaining operating time shifts. If you don't cycle the batt, the logic doesn't get updated. Battery Reset is supposed to take care of this. Since using it didn't fix your problem, one or more cells have just gone south, or there's a circuit problem, as you surmised.

It may be worthwhile trying various OF resets, which I believe work on the Wallstreet. Reset the power manager, etc. repeatedly. Maybe you'll get lucky...

If the cells have just aged to the end of life, then there's little you can do. But if it's a failure of the battery pack's smarts, then a board transplant may be worthwhile, given that you have a source of organ donors. Just work carefully, and avoid shorting the cells, if even briefly.

Btw, never solder directly to a lithium ion cell (you won't have to if you're just swapping boards, but I feel obligated to issue this safety tip nonetheless).

Good luck, and let us know how you make out.