Sounds like a combination of two things.
The first is the native res of the tv. 1024x768 is a 4:3 resolution. The only reason it's a widescreen TV is due to some shiftiness by the manufacturer. On a typical 1024x768 4:3 display the image is 4:3 in shape as the pixels themselves are square. i.e. The pixels have an aspect ratio of 4:3.
On a widescreen 16:9 panel with 1024x768 pixels they cheat and make the pixels with a widescreen aspect ratio (16:9 sized pixels), so they are elongated pixels that suit the physical shape of the display. So even though you're sending a widescreen image via a 4:3 signal it comes out as widescreen.
The problem you have (I believe) is that PC's only work in square pixels and don't understand the concept of non square ones.. When you display video this isn't really noticeable but on the desktop and with text display it is.
Secondly. When you send a signal from a set to box etc the TV itself will figure out and do the scaling in order to present the image edge to edge in the right aspect ratio. This isn't happening with the TV over VGA due to a thing called overscan. VGA on the panasonics takes the signal as is and the signal being sent from the PC doesn't contain overscan, hence you get the image not filling the screen correctly. You can fix this in the video driver using the "overscan compensation" function in the driver.
I think you'll then end up with a video image that you will be happy with but because of the scaler in the TV, the non square pixels, and the signal sent by the PC the desktop will always look stretched. This is why we generally recommend purchasing true widescreen resolution displays (such as those with 1366x768 or 1920x1080 resolutions).
Hope that provides at least a place to continue searching if you really want to do your head in with the details
Cheers,
Arkay.