Battery / Charge Problem

I have a somewhat weird issue with charging my battery on my old Acer (see sig). The battery itself isn't really so good anymore, but it still provides 1-1.5h when charged fully.
This is where the problem is located. The battery will just randomly stop charging, never at lower than 45%, never at higher than 80%. I plug the notebook in with low battery status, and it starts to charge: One light at the front indicates that, and the Windows XP tray icon as well. After some time, the charging stops, and the notebook shows at the front light and in Windows that it now runs on AC power, without charging. When I unplug it, I have only something between 45% and 80% of battery power.
Yet, when I replug it, it recognizes that obviously, as it starts to charge. At some time, it will stop again (totally random). When I un-/replug it will start again. I can repeat this until the battery is fully loaded.
When I replug it several times and the battery is fully loaded, it doesn't lose power quickly, what I mean is that the battery behaves totally normal except for that charging issue.
I googled, and it only came up with topics where a battery would stop at a fixed percentage and wont go up further, and that was probably because of a broken battery.
But I can fully charge it, and the percentage at / time after it stops to charge is really totally random.

Any clues what I could do? Are there battery test utilities, should I totally discharge it (how?), take it out for a week (why?), any ideas (google came up with lots of them, but most of them sounded pretty contra productive).

thanks a lot for your replies fellows