By power brick do you mean my laptop's power adapter?
I dont the problem could be in the monitor since when i run the monitor by itself, ie with my laptop on batteries, it runs fine.
But, you get a problem which, from your description, sounds like an interference issue. It may not be though.
In terms of interference, the VGA output from your laptop has a number of signals: Vertical and Horizontal Sync (digital), and the Red, Green and Blue (analog) video signals. Video, in this case, meaning a left to right, top to bottom raster scan.
With a CRT monitor, the video signal paths are pretty straight forward: apart from some signal conditioning, they are pretty much used directly to render the display. That is, a CRT uses an Electron beam that scans from the top left of the display to the bottom
right, line by line - a raster. The timing of this being controlled by the horizontal and vertical synchronisation signals.
An LCD monitor is, in comparision, a lot more complicated. They typically still use a raster technique, but instead of a single raster, there may be multiple - thats why you can typically point a video camera at an LCD display without having to "GenLock" the
syncs bewteen the Camera and Monitor. In other words, the LCD display has to "store" the image it needs to display, "recovering" it from the Video signal, and it's at this point that you can weird effects. - either due to "noise" on the signals or grounds,
or the algorithms/circuitry used for this. Typicially, these "effects" (artifacts) are more noticible when your running the LCD monitor at a non-native resolution. ie The video you feed into the Monitor has less "pixels" than the LCD display panel physically
Now, why only when the Power Brick is being used ?
Well, the Power Brick will be using a switch-mode design. The basic idea is that if you "digitally" switch (on or off) between two voltages, over a certain period of time, you effectively create an "average" voltage, and you can control this by adjusting the
"width" of the "pulses" within that time period. In reality, it's a lot more complicated than that, but you should get the idea.
It's that time period which I suspect is the cause the interference, and it's a design descision made by Sony. ie The only way you can "fix" this is by trying a different design - operating a different frequency.
Having said that, the power brick is not the only part of this setup that uses switch-mode power supplies. Inside your laptop, there will be separate ones for each of the 12, 5 and 3.3 Volt rails, and one for the CPU core voltage. In addition to these, there
will be one or more directly related to the charging of the Batteries, which might be the source of your problem, too. Then there's the switch-mode power supplies within the Monitor, etc.
In other words, if it's an interference problem, there are so many possible sources - it's not going to be a simple fix. So if you can't fault find by reconfiguring, then you have to start replacing things.