it could be possible that you got a bad battery. with mass manufacturing the way it is, it's bound to happen. batteries aren't that expensive to replace. whether or not you should take them out depends on their design. but the thing is, if you want the battery to keep the laptop on, and the power goes out, the laptop will go to unless you have a battery in it. so by taking the battery out, well, you get the point. it's a damned-if-you-do-damned-if-you-don't situation.
on the topic of fan speeds, i wouldn't worry about it too much. they're both controlled by firmware, and should speed up accordingly. there are ways to re-map the fan speed trip points, but it's really dangerous, so i won't go into it here, check the ati forums.