Good news - the battery cover came off with a bit of WD40. There were no batteries inside, so no corrosion.
I have more cameras than is healthy at the moment, but I may look at buying the lens. Is there such a thing as a M42 to OM-mount adapter?
There is also a 28mm Super-Lentar and a 135mm Super-Lentar with the camera. I'm thinking these are not as great as the Takumar.