The A600 is probably suffering from leaking capacitors. Look carefully to see if there is any residue near the capacitors or if any of them are looking fat/expanded.
I had a problem with A600 similar to yours and it was because of that. They may need replacing.
Regarding the A500 with the acid of the battery, remove the expansion right away. Remove the battery carefully. Clean up the mess using vinegar or lemon juice, but be careful and not rough so that you do not damage any traces. Do this for the expansion and also the a500 mother board and expansion connector if need be.
