Can you connect a latptop to a projector via LAN cable?

You can get VGA to CAT 5 baluns (you'll need 2), so that a LAN cable can be used instead of a VGA cable. This is usually done when there is a very long run needed for the cable, since CAT5 is much cheaper and easier to install. You can also get baluns for HDMI, DVI, analog video and audio, S-Video....