will i get a hd picture

I have just bought a new 40"hdtv, i also have NFL gamepass hd on my computer, i have hooked my computer to my tv with a dvi cable that i have put a hdmi adaptor on to fit into the back of my tv.
My question is with this set up will i get gamepass on my tv in hd, or will it still be in standard defernition.

Also will i be able to get the hd version of programs that are on bbc iplayer on the tv with this set up..

Thanks for any advice