1.check in safe mode (restart the computer and tap F8 on Dell logo and select safe mode). Check if the touch pad works.
If the issue still persists run diagnostics on the computer (Turn off the computer and then hold down the FN key and the power button, the computer would restart and start running diagnostics).
Also try installing Touch freeze .This Utility disables touchpad automatically while you are typing text.
2.Check with a different wall outlet. Connect the computer to a different wall jack and see if the same issue persists.
3.This issue is common with several brands of laptop, especially with the cheap Chinese adapters sold on Ebay. You can either use a USB mouse or try adapters till you find one that works. If the adapter came with the laptop, demand a new adapter from Dell.