Feeling loose is a possible source of the problem. The switch is on the rear door of the camera and the back doors are a known problem, mainly the catch breaking, but the electrical connections do get dirty and do not being able to set the mode with having a loose dial may be the problem. Good working back doors are as rare as hens teeth.
I had an issue on mine with the focus area selector to the right of the AF more selector. It wouldn’t work. After I finished the roll I opened the door and found a small piece of paper caught in the contacts. Removed it and it worked fine.
Have you tried a quality contact spray into 1st place? Did you check & cleaned the contacts between the body and film door? Sometimes, a bit of isopropanol with a Q-tip makes little wonders..as well as for lens contacts, that's how i cleaned my 5D. The good thing is, the film door is being exchangeable, unlike the F80.
My F100's are fine, working perfectly. Regarding batteries, Alkaline ones, cheaply from the local supermarket.
Thanks, same goes for my F100. Like new, both. Sometimes, it's a contact issue between the F100 body and the film door contacts, if the AF area selector isn't working.