According to the
picture, it's a Dallas Semiconductor DS1287 (the thing in the top left corner with a picture of a clock on it). This was a common chip in the day, and uses an internal 3V Lithium battery (but not the standard CR-2032 type).
I've taken apart one long ago, and found that you could pop the top cap off (don't know if Dallas allows this), unsolder the old and re-solder the new one, then snap the cap back on. If you look at the back of the "sandwich" board, you'll see that only a few of the pins are used, and two of these are for the battery, so they don't get "pinned-out" to the PCB.
I suppose you could rig up the 2032-type battery to it, but it may be too large to get the cap back on (some hot glue can take care of that problem). You could get another 1287 to replace it, but you'd have to be careful soldering, and there's no gurantee that the new one's battery hasn't died, too.
banzai
