Belinea only has one input, so you'd have to swap VGA cables to use your 360 with it. If you get a screen with DVI + VGA inputs you can connect your PC through the DVI and your 360 through the VGA.
Dunno about a cable box though, I'm guessing it only has scart outputs which aren't going to connect to most TFTs. Some screens have composite input, but obviously that's going to look pretty awful, some have s-video which might look a bit better, and some have component which would probably look decent, but standard definition cable TV is pretty low res and once stretched onto a TFT might look a bit dodgy. For whatever reason TFT monitors don't display standard definition TV pictures as well as an LCDTV. Don't suppose your cable box has any of those outputs?
You can get a cable that goes from scart to composite + red/white audio. I doubt it will look too great though. I've tried connecting my xbox via s-video/composite to my Dell 2007WFP and it looks pretty awful TBH.
Maybe an LCDTV would be a better bet, but I suspect that wouldn't look so great with your PC.