Are you sure the tv doesnt have any? It should do :\ I think the new xbox360 elites come with a HDMI cable but I can't find just the cable on the net atm...I'll keep avin a look though!
Edit: hmmm well...this is on microsoft.
17. Does the Xbox 360 support DVI or HDMI?
At the moment, Microsoft does not plan to offer a DVI or HDMI pack, but it may be available in the future. Todd Holmdahl, Corporate Vice President of the Xbox Product Group at Microsoft, elaborated, “We’re poised to hit the sweet spot of the HD market at launch and as the market matures, we will provide an HDMI for our customers when it makes sense. The reality is, you don’t need HDMI for HD gaming.” To read the complete interview, click here.
But Lik Sang are meant to be making an HDMI cable...
http://www.pocket-lint.co.uk/news/news.phtml/3368/4392/microsoft-xbox360-hdmi-cable-lik-sang.phtml