Hi! Sorry to hear about the freezing. To test it, I'd remove extended RAM, battery, and Airport, and then reset the PRAM and PMU, and see if it stops freezing. If it does, I'd add back the components one at a time, testing at each step, to see if one of them is the cause.
I've had cases where loose screws rolling around inside the case occasionally land in the wrong place and zap the board, freezing the machine...I don't know if that's a possibility.
One thing worth trying with G3s is to test for the video chip issue. With the computer on, use your left hand like a clamp and press from top and bottom just to the left of the trackpad, fairly firmly but not too hard. If this causes the computer to freeze, or creates artifacts on the screen, you have the G3 video chip issue, which generally causes the screen to go blank now and then, but which also manifests itself in other ways, such as freezing. If that is the case, there's not much that can be done besides putting a shimm inside the machine to press against the video chip and hold it together, or get it re-soldered, and unfortunately neither solution usually ends up lasting long, so the video issue on a G3 generally means it's time for a new laptop unless you're willing to put up with temperamental behavior.