How to convert apple tv's hdmi output to cat6 and back again

Hi,

I have just reovated my room and have wired in 2 x cat 6 cables from the place which i have my apple tv set up to a projector on my wall. I want to know which converter would be best and usuable to convert the hdmi output on apple tv to cat6 and then back again to hdmi to connect to my projector?

I have already bough some relitivly cheep hdmi to cat6 sender and recervers from ebay however i can only get sound to work (i.e. i can hear the sound when i press the apple tv remote) but there is no image. the projector i am usuing is a acer but will be changing this in a few weeks

Please help.

Regards

Shaun