I'm sorry to hear that you're having this issue. It sounds like you went through a lot of the troubleshooting that I would have initially suggested (such as checking the video card drivers and making sure that their up-to-date, checking the cable, changing the resolutions, etc.), so at least we know the basics are out of the way.
The best recommendation I can make would be to connect the TV to the HTPC and then going to the following menu with your remote:
Menu > Input > Edit Name > PC > [options]
You'll see that there are several options that you can choose after choosing to edit the name of the PC input on your TV. Scroll through those options to see if that vertical line disappears as you're going through them. If it does, choose that option and press [ENTER].
Those options are there for different devices that might be hooked up to the television, and since devices can vary, these additional presets can sometimes help with connecting your device and getting a good picture. It may not matter if the name is accurately describing the product that's connected (although, it usually does), because if it works, then that's the selection you want to go with.
Does that help?
Alright and now I turn to the forums... I just bought a Samsung 46" 1080p LCD TV. I only have one source from my HTPC (Dell Studio Slim 540s w/ Intel G45 graphics). For the most part, the picture is fairly good at 1366x768 through VGA. However, there is a intermittent flickering on the screen that takes up about 1/4 of the screen in a vertical line. This line flickers in and out while watching TV in Windows 7 Media Center. It doesn't matter if the content is HD or not. Also, while on the desktop, the line becomes visible if any windows are placed or dragged through this region on the screen.
I have also tried hooking my laptop, changing out vga cables, checking drivers, changing resolutions, etc and nothing seems to work. I checked the tv by hooking a Roku DVP via HDMI and there seemed to be no issues.
Help! The TV is 2 days old and I am getting hassled be Samsung and the retailer about replacement!