8800gt should have twin DVI ports, not VGA. Look on your TV for the DVI setting under output. After getting it all hooked up on my 8600gt I had to reboot before it would detect the TV.
Hooking the TV to the PC would be the ideal way to do it. Some monitors have a built in video switch. If yours does, there will be a switch on the monitor to switch to a second PC. That's more than likely what that port is on your monitor. At any rate, you'd never be able to access any of the video cards features for the secondary display if the primary monitor had a passthrough port (which I've never seen).
Most likely your monitor has 1 DVI and 1 VGA port. These are both inputs, so that you can connect your PC to one or the other depending upon the type of video port your card has. The VGA port is not an output, so it will not send signal to your tv.
Once you get it hooked up to the PC you should be fine.