You can loose the AGA if the battery leaked and damaged one of the 2 first IC left from the battery(I think it is the second one but I am not sure). If the battery leaked and it was not properly cleaned, it means each IC lift up and clean the PCB under. Then with time the remaining acid can damage the ICs and/or tracks and avoid the A4000 to boot in AGA, only ecs would be possible. if I were you, I would first go to pref time and look if it is possible to save the time. If not, you have battery damages...
Yes, there was a leak.
