I just fixed this issue on a Magnovox 19" LCD. My first suspicion (like most) was that it was the PSU since it seemed power-related. However:
Checked the logic board for bulging caps and replaced C112, C117, & C118 with great success!
FYI: I guess if you don't have a soldering iron, you won't bother, and if you do, you know what a cap looks like, but either way, caps are rated in Farads, so you'll find a rating on caps such as 1000uF (1000 micro Farads) or 200pF etc. Other than that you can look up their distinct (albeit varied) appearance on wikipedia. Make sure that your replacement caps have the same value and an equal or (better yet) higher voltage than the broken ones. Do not confuse milli with micro!
Got this solution from FixYa and it sounds like it's pretty common among these crappy items they're putting out now, hopefully this will help with many different brands.
These manufacturers are crooks and a disgrace.
Unfortunately, it does the same thing as always. After some online research, I learned that many people are having a similar issue with their Gateway monitors, and are getting no help at all from the manufacturer. Looks to be fishy at best...
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I had all of two seconds once it switched on to select the brightness menu and adjust it by one notch. This meant switching it off and on several times but it worked well fine eventually!