Every PC over two years old that crosses my bench, gets a new battery.
I buy them from a battery supplier for just $1.20 ea., so it's really no big deal.
It's the CR-2032 coin type battery that you can find at most drug stores on their battery rack for about two bucks. In a crunch, I've run down to WallGreens and picked one up.
That way I know for sure, that if the PC does something goofy, it's NOT the battery.
When removing the battery to clear the CMOS memory, its a good idea to remove all power from the system and remove the battery and leave it out for about 20 to 30 minutes, before putting it (or a new one) back in.
If the ram sticks get dirty, your OS can get really crazy. Cleaning them on an older machine is something I do a lot. I recover several pieces of ram every year by just cleaning them.