Looks like the battery isn't too bad, and you have caught it just in time. Just desolder it and replace it with a lithium holder so you can replace the battery in the future without soldering and the worry of leaking!
Because the CR2032 (mainstream mobo battery) cannot be charged, you need to get one with a diode in-line to prevent it being charged i.e.
http://cgi.ebay.com/COIN-LITHIUM-BATTERY-BACKUP-AMIGA-4000-3000-2000-/270662763944There are other lithium coin batteries used on Blizzard boards etc that can be charged but I am not sure if the A4k mobo would charge them right so I would probably down the CR2032 route. They last 3 or more years before needing to be replaced anyway.
