Ok, So I've got a gateway FX p6860

1.83 dual core
Nvidia Geforce 8800m GTS
4 gigs ram
320 gig harddrive(probably irreleveant, but anyway)

Ok so my computer can handle most games at full or almost full settings, such as mirrors edge, far cry 2, games like that. When I try to play some games, however, if I have my battery in and its plugged up, my computer shuts completely off. All of the intense games make my computer hot, but when I play fallout 3 and halo 2, my computer will shut off, being less hot than when I play another game such as mirrors edge or far cry 2. If I take the battery out, my computer won't shut off when I play the fallout 3 or halo 2. On the other hand, if I try to play far cry 2 on only battery, my computer still shuts off, but never when plugged in. then when I go to turn the computer back on, (again, only on battery only does far cry 2 shuts my computer off) the battery says its still got plenty of power. Whats up with that?

Should I just take out the battery and have it plugged up when I game? and is this normal?

I suspect it has to do with excessive heat.
Has the fan been serviced?