Hi! I've experienced this problem mainly with Samsung laptops. The units would work fine when on battery power, but the touchpad would become unresponsive or behave erratically when the computer was plugged in. This occurred with both Synaptics and Elan touchpads. I tried partial restores, full system restores, updating drivers
, contacting the techs (who couldn't resolve the issue even when taking control of the laptop), and finally sending it back to Samsung's service center for repair in the event it was a hardware issue. After a week they sent it back with an invoice stating that they were unable to replicate the problem, and were therefore unable to do anything.
After a week of research, fingers crossed, I think I finally have it working correctly now. I had the power brick right next to the computer. Apparently this can create static/interference that impacts the touchpad. If your situation is the same as mine, the two things I would suggest are:
1. Move the brick as far away from the computer as possible; and
2. Try plugging it into a different outlet.
I hope this helps. Good luck!