The fact that this only happens when on AC power is a bit concerning. I'd call Dell and get a replacement.
The problem is likely related to the controller for charging the battery. You could test this theory by unplugging the battery while it's plugged in and see if you still have the problem.
The other thing it could be related to is the inverter that runs your backlight. Most laptops will brighten the screen when on AC power. If this is the case, you have a potentially very dangerous situation on your hands. This is probably unlikely though, since you would likely be getting strong shocks no matter what.
In any case, call Dell and get a replacement. Also, don't use two hands at once on your track pad.