In that system, it is pretty much good for the clock and that's about it.
Any custom settings you have setup in your BIOS will be wiped out though (BIOS password, boot priority....)
To dissasemble the Gateway Solo 9100: first: remove the: floppy/cd/dvd drive and, the battery: the latches are on the bottom of the laptop; then the hard drive door in this order or, you will break the hard drive door. next:remove the hard drive by pulling straight out on it's flap. open the lid of the laptop, swing it all the way back; at the bottom edges; near the hinges you will see two black round screw covers, remove these with a sharp knife blade and, remove the two miniature phillips screws; then remove the hinge covers by pressing in on them and rocking them off... now you may: using a credit card; split the screen bezel and, remove it. (this is for screen access only.
If you must remove the led screen: remove the led on/off switch cover by: placing one thumb on each end of the cover strip and pressing down hard while pushing the strip to the left, remove it. the plugs to the screen will be visible: unplug them; making sure you remove the left plug grounding screw, then: the hinge screws; if further dissasembly is needed: remove the keyboard bezel by removing the upside down screws located above the bays in front; then: remove the small black screws in the back of the laptop under the rear docking cover: remove the bezel and, keyboard and, the rest of the dissasembly is routine with the exception of the motherboard which is held in by a rubber plug that is right next to the usb ports and, looks as if it covers a third usb port: it holds in the mother board: (sneaky huh?) wedge it out with a screwdriver then: remove the extention buttons on the pcm/cia card slots by pushing up on the metal strip on their undersides and, slide them off; push in on the buttons and, lock them in the retracted position: so, they clear the laptop case. The rest of dissasembly should be: routine...
I'm not sure how far into those instructions you will need to get before you see the battery. But it usually just looks like a round watch battery. It will be fairly obvious when you see it