LED Backlight Strips on TV Causing External Speaker Interference

This could be a bunch of problems, from a missing ground to a voltage spike, to dying speakers, etc...

First of all, it would be helpful to rule in/out the computer as the source of the popping. It's possible your computer's sound card is not great and is sending those noises to the speaker, which is faithfully playing them. Try plugging the speakers into a different device (e.g. an iPod), AT THE SAME OUTLET. Then see if you get the popping noises.

If you still do, try moving the speakers to a different outlet somewhere else in the house. Event though the light switch doesn't control the computer's outlet, they could still be on the same circuit and causing some other kind of interference.

If moving the speakers to a different outlet solves the problem, there may be issue with the wiring. (Could be the switch is bad and is causing a ground fault or something. Or maybe the unused switched outlets are bad. Or something else.)

As @Tester101 says in his comment, problems with the ground can cause audio issues. Do the speakers have a ground pin (3rd prong), and if so, is the outlet properly grounded? You can also get so-called "ground loops" when different components have different grounds, which can cause a voltage difference—are the computer and speakers plugged into different outlets?

An outlet tester is an easy and safe way to do quick sanity checks on outlet wiring. You just plug it into an outlet and the lights will tell you if there are some common wiring problems. If I were you I would pick one up and test all of the outlets, including the unused switched ones.

Romex is not supposed to just stick out of the wall. Any in-wall wiring is only supposed to connect to out-of-wall wiring through a junction box. The cleanest way to do that is to put in an electrical outlet.

You can get retrofit junction boxes that just hold on to the drywall, which makes it quite easy to add an outlet.

_{(source: homedepot.com)}

Also, those power supplies may be way overkill. How much lighting are you planning to install? I just installed about 8 feet of strip LED lights and it's using about 2 watts. If the power supply is over-rated by 10 times, it's wasting power just sitting there turned on.