Before you go to the trouble of packing up the computer and shipping it away I would personally try to make sure where the problem is. You have three separate things that can cause this problem - the monitor, the computer and cable that connects them together.
If you have another computer in the house which uses a similar cable to the one you're using for this monitor try swapping them. See if the problem moves with the cable.
It's not very common but it does happen that a cable goes bad. (This is an odd coincidence because although the symptoms were slightly different I had the same problem a few hours ago and fortunately had a spare cable handy.)
Worth a try anyway and a cheap and easy fix if it does turn out to be the problem.
Next step would be to swap the monitors and see if this time the problem moves with the monitor. If it does the problem is obviously the monitor. If the problem still remains with your computer it is sending a bad signal. Almost certainly this will be the on board video or the video card at fault.
There remains only one faint possibility and that would be a problem with the receptacle that is supplying power. This is very unlikely but using an extension cord to get power from another location would also eliminate this possibility.
Good luck.

Please, I need help with my computer monitor. I has a smeared look to it. (Photos are attached.) It has a look like someone wiped their hand across a wet photocopy. Not so much a blurred look, but a smeared, shadowy look.

I did a google search for help and tried their solution to adjust the screen resolution. That didn't help. The problem is, it comes & goes (but seems to be the new default appearance). Sometimes when I'm reading text of something it will disappear on its own, and then comes back. It is especially annoying when trying to "develop" images in LR5.

I'm running Windows 8 on a Dell XPS 420 computer, with a Dell 22" widescreen monitor. But it did the same thing when I was running the original Vista that came with the setup.

Any help/suggestions appreciated. Thanks in advance.