Newbie here. My Imac is doing this.

Imac 21.5" (mid 2010) 3.06GHz/16G RAM/500G HD. This is an ex-display model (which in itself may suggest something to you tech wizards) which I bought only 6 weeks ago. It came with Snow Leopard and this screen crash occurred more than once on day one. I immediately upgraded to OS X and it was stable for a few weeks so I was reassured but exactly the same screen problem has recurred recently.
The screen does this apparently randomly, i.e. when sitting untouched, when online and when mid-game.
I have:
-verified/repaired HD (no probs identified)
-repaired permissions
-reset NVRAM
-run fan control app (all 3 fans respond to increased revs, temp max 55C)
-run GUI memtest ("rember") = no probs with RAM
-then CLEAN INSTALL of os x and repeated all of the above
-run apple hardware test (basic = no probs found, more complex = has been unable to complete as this issue has developed on three consecutive attempts mid-test)
Forum wisdom I've come across so far has left me unclear as to whether this is hardware or software. Clean install suggests hardware, but apparently this is highly unlikely.
No apple care but extended retailer warranty theoretically covering this but naturally I anticipate they will do everything to avoid taking this on. Plus I want to make a good case for when I phone them by exhausting everything I can do myself so hoped someone out there might be able to offer some other interpretations of this problem or suggestions.
Kinda out of ideas here.
Thanks.

Imac 21.5" (mid 2010) 3.06GHz/16G RAM/500G HD. This is an ex-display model (which in itself may suggest something to you tech wizards) which I bought only 6 weeks ago. It came with Snow Leopard and this screen crash occurred more than once on day one. I immediately upgraded to OS X and it was stable for a few weeks so I was reassured but exactly the same screen problem has recurred recently.
The screen does this apparently randomly, i.e. when sitting untouched, when online and when mid-game.
I have:
-verified/repaired HD (no probs identified)
-repaired permissions
-reset NVRAM
-run fan control app (all 3 fans respond to increased revs, temp max 55C)
-run GUI memtest ("rember") = no probs with RAM
-then CLEAN INSTALL of os x and repeated all of the above
-run apple hardware test (basic = no probs found, more complex = has been unable to complete as this issue has developed on three consecutive attempts mid-test)
Forum wisdom I've come across so far has left me unclear as to whether this is hardware or software. Clean install suggests hardware, but apparently this is highly unlikely.
No apple care but extended retailer warranty theoretically covering this but naturally I anticipate they will do everything to avoid taking this on. Plus I want to make a good case for when I phone them by exhausting everything I can do myself so hoped someone out there might be able to offer some other interpretations of this problem or suggestions.
Kinda out of ideas here.
Thanks.