I have run the camera through all of its settings and shutter speeds. Everything seems to work. Aside from the battery cover, the only problem seems to be dust.
I have tried to unscrew the cover with the proper coin. Used both a US Quarter (25¢) and a US Nickel. (5¢) Nothing seems to work. Any more force will risk damage. It's stuck on pretty good.
I will use a cotton swab to apply the liquid. First, I will wipe the outside clean with just plain water on a cloth. Then I'll swab a few drops of penetrating oil like "Liquid Wrench" on it and let it sit for several ours and try again.
You are right about the possibility of corrosion inside the battery compartment. I have been cringing at the thought of what I might find. I have the tools to make basic repairs but after taking the cover off and looking inside I might decide to quit and look into the cost of repair or replacement.