Welcome to TFP! Sorry to hear about your plight with the mice wreaking havoc with your heater and related electrical system. Not having experienced this problem, I cannot give first-hand advice on whether a new control board will solve the problem but someone will likely be along who is able to.
I can, however, offer a few tips on avoiding future bouts with mice. Mice and rats are opportunists and are usually attracted by a food source. If you have an outdoor grill, I would make sure it is kept very clean - including the grates and the inside of the grill. After grilling, run the burners on high for about 5-10 minutes to burn off any leftover food. Scrape the grill grates towards the end of this burn off. If you are afraid that you might forget you left the burners on, set a timer. Once the grill has cooled completely, remove any particles of food at the bottom of the grill and remove any drippings that may have worked their way onto the patio using a solution of bleach and water. Once they have a food source, the next thing mice will look for is housing near that food source and a pool heater can serve this purpose very well. Assuming you don't have outdoor pets, you can use mice/rat bait pellets near the heater and pool equipment. If you do have pets or don't like this alternative, you can try raw peppermint oil which you can usually get at a health food store. I've heard of numerous success stories using this approach. It's relatively inexpensive and worth a shot. Simply apply several drops along the base of the heater. Also, if you do have pets and feed them outside, take up their food dish immediately after they are done eating.
None of this is an absolute guarantee that you will never have a mouse problem, but it will make your yard much less hospitable to these critters. Wild animals will usually take the path of least resistance and will seek out places that are attractive to them.
