I've been having this issue with my M1730 since I got it close to a year ago. The power cord loosely fits into the computer. If I jiggle it, AC power shorts out (on and off). If something touches the power cord, it fall out of the computer. The weight of the power cord (not the adapter which is huge) is enough to pull the power cord out of the computer.
I've had the motherboard and power supply replaced three times each, and the issue still exists. Dell states that this is not a design issue so I will continue to have my motherboard and power supply replaced every two weeks until I finally get working components or Dell redesigns the faulty parts.
I spent about $4600 on this laptop and find Dell's handling of the problem completely asinine.