First off where are you buying your batteries from?
Secondly you say the battery was last changed a couple of years ago how long was it before that?
My guess would be that it is the main PCB, lofts are not really the best places for electronic components, they are subject to extreme heat in the summer and cold in the winter all that expanding and contracting doesnt do anything any good. This on top of the fact that the panel is at least fifteen years old and nothing lasts forever especially when you consider that its been on even when its not set, I would be happy if I had got that life expectancy out of a fridge .
You could try breaking down the circuit board to component level to try and work out which bridge rectifier or transistor is failing, but its unlikely you will get help with that here, the time it takes to diagnose a fault to component level versus the cost to replace the cpu is far outweighed, so most engineers only know how to replace panels. The other problem is you really need an oscilloscope and the knowledge on how to use it a multimeter will only tell you the basics