The two things I'd vote most likely, cinsidering the age of the machine: 1) The CMOS battery. I've ad all sort of wierdnesses occur when a battery is giving out.
2) the capacitors on the motherboard. Heat can dry out the electrolytics on the motherobard and cause the exact sorta problems you are experiencing. If you've got good electronics chops, they can be replaced, but paying to have it done is probably not worth the expense.