I've had my E193FP monitor for ages and have had this power plug problem the whole time. The first time I replaced the power cord, it worked for a while, then started doing it again, so I jiggled it until it worked and then taped the plug into position using Gorilla tape, which is black and therefore less ugly than duct tape) and did the same to my ST2010 monitor, just in case. I *never* move them, and as a result, often have neck strain because I can't move them to adjust for lighting and so on.
Taping them and not moving them worked for a while and this morning it happened again to the E193FP and I couldn't jiggle it back. Since I don't have any more spare power cords, I swapped the cords with the ST2010 monitor, and that works. That is, I took the cord from my ST2010 and put it on my E193FP, and vice versa.
The plug I that wasn't working on my E193FP works fine on the ST2010 monitor, so I think it has to be a problem with the prongs on the E193FP itself. It's way out of warranty, so there's no use contacting Dell.
So, for those of you who have this problem, I suggest always having a spare cord (I put it on my shopping list) and use a strong tape on the back to tape the cord to the monitor so that it won't loosen if you bump the desk (yes, I, too, have had that experience).
