I'm not sure how the genius was in the right here at all. He didn't and couldn't run a diagnostic on the machine to prove or disprove that the problem was the video card. So to deny coverage at all when they didn't properly verify that there was a coverable issue?
if the genius can't run the diagnostic its because the machine isnt booting. if the machine isnt booting its not a "no video" condition its a no boot. no boot conditions aren't covered under the REP. end of story