the laptop is connected via the vga external d plug hence the keys required to swap to that connection from the TFT connection. Your PC graphics out is probably the same d plug as yopu use to your monitor.
Is your TV just a 'standard' display, i.e. not high-definition?
If it's a standard (PAL) display, that's 576 pixels high so it's possible that the graphics card in your PC may not have a compatible screen mode for that. In which case the display may appear oversize (e.g. 800x600) - or no display at all.
It's worth trying though, but maybe the graphics card user-guide can give you more info on what screen modes it will support. HTH.