Symptoms of a failing battery: USB locks up, no input from mouse or keyboard after computer has been idle for a while, but previous screen image either persists or blacks out (except for mouse pointer, at times). Batteries are cheap at most pharmacies, look in the hearing aid battery section, number 2032.
A couple of things I remember: If you went to Home Depot, you could find a clamp with a thin plate ends that would fit in the groove around the back case, and all you had to do was squeeze the clamp (i.e. open the clamp) and glide it around the groove until the case popped open. Much easier than trying to use a spudger (or, like many of us, marring the case with a screwdriver). On the analog board, the 4 pin molex plug was the frequent overheating spot. It drove the high voltage into the CRT and the heat would melt the solder and subsequent cooling would cause a cold solder joint, which meant your video would go in and out, and whacking it on the side sometimes restored it.