Well, let me clarify this, you need to output Video AND Audio through VGA from your PC, and have it link up to multiple (please be more specific) TVs that have HDMI, VGA, and Coaxial input. Please be more specific on The Coaxial inputs, what kind of input does the TV take via coaxial. Somehow CAT6 and LAN comes into this? I dont know about that. Also, any other outputs that your computer may have or inputs that your TV may have may be useful, because so far if your computer only has VGA output then you aren't going to get any audio output.
Plus, you are definitley going to need to invest in something that can convert, which probably be particularly expensive since you are going from Analog to Digital. It might be cheaper to just buy a new Video Card for you Computer, and then just use a couple cables.