Long time since your post, but if you're still there ...
That's the backup battery for the memory settings. You'd be hard pressed to find an exact replacement - I know - I've tried. I dug up the specs for the original, and this is the closest I came. Different package, but it should do the job with a bit of clever fudging.
http://www.mcmelectronics.com/product/PANASONIC-EECF5R5...
Reason I said "should", I did get one recently, but haven't gotten around to installing it yet. The memory on mine still works ... sort of ... although it's gone intermittent, and I don't see the corrosion issues you have. Sometimes it works, sometimes not. I'm only using one EQ setting, so no biggie to re-enter the settings from a crib sheet for now. Be a winter project.