My comment comes a little too late to help you but you should never try to clean up acid-damaged components by adding more acid. Vinegar and lemon juice are pretty strong acids and can damage components on their own, without the help of the acid that has already drained from the battery. You should have used baking soda to neutralize the acidity.
As noted, the damaging barrel batteries of that era contained lye or potassium hydroxide (KOH), common car batteries use acid. As you may remember from your freshman college chemistry course, Many different chemical reactions occur due to differences in the electrical charge potentials between the molecules. These can be used to generate a charge.
Simply put: White vinegar is simply acetic acid with no left behind Apple goo; lemon juice contains citric acid with the lemon goo. Baking soda or NaHCO3 (sodium bicarbonate) is a pure base. One neutralizes a base (lye) with an acid and vise versa. As to whether on wants to leave behind an organic fruit goo, is a personal choice, but not my personal choice.
Back on topic, I would pull the A3000 schematics off the net and use your multimeter to check continuity of the traces in the affected motherboard area around the battery. There are several folks in the forums with expertise is diagnostics and repair.
