Even if there wasn't battery leakage, all the aluminum can capacitors would have to be replaced because the electolytic fluid leaks out. The procedure is to remove the old caps, remove all socketed components (ram, rom, etc), then wash the board in distilled water and a small amount of liquid dish soap by soaking and agitating a bit. In order to help dry the board, you can rinse with isopropyl alcohol, though it's an optional step. Blow out the sockets with canned air to help get the water out. Then let it dry for a few days with a fan blowing on it. Then install the new capacitors.
Normally people wash the board with the capacitors removed in order to wash the goo off from underneath them. But in your case, I guess you'll just wash with the capacitors still on, since it doesn't make sense to remove them again.