I have bought a card like yours about 3 months ago from a shop in Romania, wanting to replace a Gigabyte GTX 680 OC Windforce 3X.
Being used with the previous Gigabyte cards overclocking ability (the 680 worked flawlessly from 1137/6000 to 1250/7200), when I first installed the GTX 780 TI I tried to raise the clocks from 1150/7000 to 1250/8000 and I got an instant shut down (maybe I exaggerated a bit
) Afterwards I tried a more conservative OC but the issues persisted and the card crashed instantly when I tried a game or a benchmark. All these things happened in the first 10 minutes after installing the card in the system.
Afterwards I reverted all the clocks to stock and tried a benchmark (I still wanted to return the card because I thought it was unacceptable not to be able to OC the card even 1 MHZ..I had all the cards from Nvidia since Riva TNT 2 in 1999 and this has never happened to me)...
3D Mark 2011 seemed to work fine but in the Game Test 2 I saw random blue artifacts for a fraction of a second...the score was OK, but still those artifacts bothered me. Then I tried a few demanding games such as Cysis 3, Tomb Rider, Battlefield, Batman Origin but I got crashes after a few minutes of playing (I think Tomb Rider and Batman crashed immediately - in a matter of seconds)...
I lowered the clocks and ran again 3D Mark 2011 with Game Test 2 in loop mode...in the first 2-3 loops the artifacts disappeared but from the forth they appearead again and ultimately in loop 5 or 6 the FPS lowered to 1/4, as if the card was in throttle mode. Conclusion: no matter of the clocks, the card was still useless.
I think I tested the board for about 2-3 hours and had more crashes than all the previous cards I owned in 15 years. The following day I returned the card to the shop and they sent the card to the Gigabyte service. In two weeks time (I don't know why it took them so long) I got the answer that the card was defective and couldn't be fixed and they gave me 2 alternatives: to give me another one or to refund the money. I decided to go for the money, because I thought the chances to get another defective card were too high and I didn't want to wait for another 2 weeks...
In conclusion, there are 2 things that can be improved: the quality testing of the cards before being released from the factory and the time required for a card to be tested in the Gigabyte service (2 weeks seems a bit too long for me)...