Sorry for not replying for so long but my graphics card died.
But I managed to get a refund and put the money towards buying a 8800GTX!
After installing this card on the latest beta drivers, the old problem has gone!
Though X-Com still doens't work...
Whereas before the image was displayed correctly but violently vibrating up and down (plus a small horizontal line of a spectrum of colours at the top of the screen), now the image is completely garbled. :S
The Longest Journey on the other hand works perfectly!
I don't know if the new drivers, card or both fixed that but anyway it's fixed.
What doesn't make sense to me though is that these games would not work on the former setup on my current TV, but did on the old one. The PC was exactly the same for both TVs, yet only faulty with old games on the new one. This makes me think it is more likely that the drivers were at fault but I don't know. They were the latest official nVidia ones, rather than the new beta set.