Video capture software works by recording the signal that is being sent to the screen. The only connection you can make with your TV is to send video to the TV, in order to record regular TV you’d need to intercept the stream coming into your house from the cable / dish / whatever. Which is not a standard application, so i doubt theres anything you could pick up in a shop.
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No, not just using capture software, and not by connecting the PC to the TV. If you do that, you’re just sending output from the computer TO the tv.

To record live TV, you would need a video capture card that has inputs for either coaxial, RCA, S-Video or DVI…basically some way of getting a video signal into your computer. You would then direct capture software to record what it sees coming from the capture card, which would, in turn, convert that signal to a video for playback.

A good, cheap video capture device can be found here:

http://dvr.about.com/od/capturetvwithacomputer/tp/toppick1.htm
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The TV capture card usually has capture software, but you can easily find some on the WWW that are free or inexpensive.
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However, some PCs have the capability of having a cable wire going straight into them so that your monitor can double as a PC monitor and a TV. If you had that sort of set up, it may be possible, though I’m not sure because I’ve never tried it myself and have never heard of anyone trying it.

As far as connecting your PC and TV so that your TV acts as your PC monitor, you would not be able to record TV with screen capture software.
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