I think from both. But from the sun is worst. It gets a few micron into the plastic. That's why you have to rub it off.
BTW: You DID pull out the battery, didn't you?
i'm not sure to have understood the question, anyway . . .
The first battery has been replaced under warranty in 1992-93 or so (don't remember now).
Then another one . . . mhh about 7-8 years ago (during a repair- Paula replaced) and recently i've replaced it after some rework on the mobo.
Why?