When Windows has started and the 32" screen loses the image, does it come back up if you disconnect the other monitor, or only if you boot up with just one connected?
Using a Y-splitter, two screens are loading the VGA output, reducing the signal level. It may be dropping below the "no signal" threshold of the TV. I use a splitter at work as a convenient way of test-running two monitors at once, but some monitors shut off because they don't detect sufficient signal.
Alternatively, when Windows loads, the resolution may be too high for the TV, although you say it will display if only one connection is made, so you may already be using the TV resolution. If you haven't already done the experiment, try setting the computer to something low like 800x600 60Hz, and see if the TV displays that when the other monitor is also connected. If it does, you really need to use a video card with dual outputs, so the monitor and the TV can be running in their appropriate resolutions. For example if the monitor resolution is 1280 x 1024, a 1366 x 768 TV could not display that, but in your display settings for a dual output video card, the TV resolution could be set correctly (1360 x 768 would probably be the choice in that example).
Edited by Platypus, 29 March 2008 - 07:28 PM.