Hi Karen,
Sorry that the PMU reset didn't help--usually it does. It may be worth trying again.
I assume that you have a third-party battery, since I don't believe that you can still get original Apple batteries. I have a third-party battery in my MacBook Pro--a NewerTech one from OWC. I had similar problems, and when I called, they had me reset the PRAM:
http://support.apple.com/kb/HT1379?viewlocale=en_US
That seemed to fix it, but I recall that you are reluctant to do that because the last time you tried you got a kernel panic (prohibitory sign). However, if you do have a NewerTech Battery, it may be worth calling OWC tech support on the phone and see if they have any suggestions.
One question. Your battery isn't at zero %, and you said it was recently in the 90% range, so I wonder if it does charge intermittently, but that the charging cycle doesn't get triggered until a much lower percentage. Or something along those lines. Or maybe doesn't charge when your computer is asleep, but only while awake? I know that my NewerTech battery doesn't seem to want to charge if I plug the power adaptor into my MBP when it is asleep. However, once I wake my Mac up and start working, the power adaptor eventually starts to charge the battery. It's possible that your battery also has some similar quirks.
For the iBooks that absolutely will not charge a battery no matter what, the culprit is often the DC In Board, which is what contains the power port. It can be replaced, but I suspect that a DC-In Board for your Tangerine model would be difficult to find and probably rather expensive. What happens is that the solder joints are stressed from plugging the power adaptor in and out, and they crack, leading to intermittent contact. The usual sign of this is that you have to wiggle the power adaptor end to get it to make good contact, and the more you wiggle it, the worse it gets. However, that doesn't seem to be the case with yours as far as I can tell.
If your battery is from OWC, I'd recommend you call the and see if they have any other ideas for getting it to charge properly. If it came from somewhere else, post back with what it is and any information you can get from the System Profiler.
Good luck!