It may not be the battery, but instead it might be that there is a problem with the connection for the AC adapter on the main (or daughter) circuit board, so the h120 isn't getting power or correctly charging the battery. You had mentioned you're not getting a green light -- when you left it plugged in for a week, were you ever getting a green light?
If you're not getting a green light, it probably is not charging correctly, so the battery isn't necessarily bad, it is just near completely uncharged. I had gotten a broken h120 that had this problem, and also had a broken h120 previously where the reset circuitry ripped off the board. Can't remember which problem was on the main board and which was on the daughter board, but either way, each problem was on a different board. So I took the one working board from one dead h120 and the other working board from the other dead h120 and rebuilt one working h120 from the 2 dead ones.
Anyway, I mention because I've seen a problem much like what you described, and it wasn't a bad battery or a bad HD, but instead was a problem with the AC connector inside the h120.