Curmudgeon:

If you haven't send the "new" HP back, you might want to try this first.
I had the exact same problem with a new HP a few months ago.
Rather than send it back, I had a friend take a look at it first.

He opened it up, removed the video card, re-inserted the video card and turned it back on.
It worked fine and has been working fine ever since.
He's an experienced tech but said he'd never seen this problem before.
The card looked to be in "brand new" condition and was obviously seated correctly
since I used it for about a month before it "went south"

Worth a shot!
Good Luck!
LLOYD S