UPDATE - I had the battery replaced by a computer technician, since I have already that I am not hardware kind of guy...I know that's an oxymoron having an old school computer now.
The technician found some signs of leaking, but not on the actual mother board, it was starting to crawl upon one of the chips adjacent. He cleaned the connectors and they look good now. There wasn't any apparent damage to the motherboard.
The mouse got a bit better by a 50% but it still jumps back to the left of the screen once I move the pointer to the center of the screen.
I also cleaned the mouse ball with soapy water and dried it well. I cleaned inside the mouse with a q-Tip and rubbing alcohol. I also used compressed air to clean the mouse inside and connectors in the cpu and terminals.
So what can I do next to fix this issue?
ADDITIONAL Comments: I noticed that when I first booted up the computer, the mouse worked fine for about 5 minutes, then it started to jump all over the place again. It happens when I scroll to the center of the screen. The pointer (cursor) always lodges back to the left side of the screen. When I move it to the center it flies back to the left edge. If moved fast to the right, it reaches the far right edge, disappears as in blinking, and reappears on the left hand side of the screen. I hope this more detailed description helps to illustrate the problem that I am having.
After trying this tips shared by Hypex at AmigaWorld: mouse short cuts. LAmiga Alt for left mouse. RAmiga Alt for right mouse. Ctrl + LAmiga + cursor should move. Shift for high speed. IIRC, and seeing that the cursor moves fine, I'm guessing that I may be in need of a new mouse. Unfortunately, I don't have a spare one to try.