Hello,
If there is corrosion, you will need to remove the battery holder and neutralize the board with vinegar. I am assuming that you know there is corrosion, but the machine works fine?

From there I would install a new battery holder and then get a "no solder" remote battery holder from Rob Anthony. http://lockwhenlit.com/products.htm

That should keep it running for many years!

--Scott

The reset issue is most likely due to your 5 volts dipping too low. If everything has been neutralized, I think you are safe to leave the current battery holder in place. You should, however, come up with a way to make or purchase a remote battery pack for this machine.

You can build you own, but I would not solder anything to the board unnecessarily. This does not mean that you cannot solder the wires directly to the board, I would just personally look for other, easily reversible, options.

Hope this helps! Congrats on the new game.

--Scott

The WPC driver board supplies the 5v to the MPU. I would check the test points on your MPU to see if the 5v is dipping. If so, then the transistor, bridge rectifier, or capacitors on the driver board could be the issue. If not, check the power connection from the driver board to the MPU and test the voltage on the MPU side.
--Scott

That sounds more like you have an issue with your MPU. That picture you posted is also indicating that the alkaline from the leaking battery has NOT been neutralized and cleaned.

What do the chips look like below the battery holder?

--Scott

OK. You can use a soldering iron to de-solder the battery holder, but you will need to pick up some solder wick. It is a brass material that will "soak" up the liquefied solder when you heat it up with the soldering iron.

Here is a video on how to use solder wick.

--Scott

Agreed 100%