If you're trying to do this with HD video/HDMI, be ready to spend A LOT of money. Doing it using SD video over composite or component is a lot more doable, however you're going to be hard pressed to find something that will work over IP (using either HD or SD, without spending big money). Instead you might want to consider using the Cat5 cable with a balun to put video over it (assuming you don't need the same cable to serve other IP traffic). Then you can use a scan converter to go from VGA out of your computer to video.
Edit: Also check out digital signage solutions, there are probably some that do exactly what you want.