I'm still not fully convinced that the graphics card was at fault. What is the manufacturer and model # of your power supply? What are the rest of your specs, including your new graphics card?
In my opinion, the issue could be the power supply having insufficient power or unreliable power delivery. The issue could also have been your GTX 780. Speaking of which, when did you purchase the GTX 780? I ask because it officially release in May of 2013. Many vendors have a three year warranty period on it. If the issue is indeed the GPU, I strongly encourage you to reach out to the vendor and submit a warranty claim. When they replace your card, you can then sell it to recoup part of the cost of the new one.
Addendum: I just re-read your response, and see that you already stated that you owned it for four years. But since the card hasn't even been on the market for that long, chance are that you've over-estimated. I still recommend that you contact the vendor and inquire if it's covered.