If you settings are holding, you've got the batteries in the correct way, so no worries. If your settings are holding, it also indicates you don't have much (if any) problems with corrosion, so that's also good.
If it was just rust and not exploded caustic crap, another positive.
Based on what you've said, the "standard" repair would probably be to replace the battery holder. The benefit there is you would be able to look underneath the holder, because that's where your traces generally start to get eaten up.
But I know that's not going to happen now (don't blame you - put it on the list for later). So just inspect the holder, and if you see any issues scrub it down with a 50/50 mixture of white vinegar and water (use a toothbrush). Let it sit on there awhile to neutralize the "acid". Then clean it good with fresh water, final rinse with 90% alcohol. Let it dry real well (hair dryer if you are impatient) and you should be good to go for now.
Yes, I'm telling you to put a liquid water mixture on your computer board. I don't go crazy and I try to limit it to the area being worked on, and I try to avoid any socketed chips. But it's standard procedure, and it won't cause any harm. Most of these boards are actually dishwasher safe, so no big deal. (don't put a relay in a dishwasher!). Anyway, just make sure and let it dry before you fire it back up.
based on what you've said, I'm suspecting no big problem here, so just keep info for future reference. Enjoy!