Dell Inspiron E1505 Trackpad does not work on power

I have a 4 years old dell e1505. A few weeks ago the trackpad stopped working (i.e. started sending random events to the system and getting stuck).

I dual boot into Windows and Ubuntu so this is not a driver issue, as it is occurring on both operating systems consistently. I read about draining flea power and that did not work either. What did work was that on running the system on battery only (no adapter), the trackpad works like a charm. As soon as I connect the power, the trackpad goes back to behaving erratically. 

Any help is appreciated. I am using a USB mouse for now.