Question Is my GPU dead?

[Cal9099]

• Processor (CPU): Intel i7-4770K
• Graphics Card (GPU): GTX780 (& Intel HD Graphics 4600)
• Motherboard: G1 Sniper Z87
• RAM: 24GB DDR3
• Power Supply (PSU): Corsair RM650

Earlier on out of nowhere both my PC screens went black (can't recall if audio was working or not) but the PC was still running. I hard reset it and only one screen was working on reboot and the resolution had been lowered, a sign that the integrated graphics card had taken over.
Sure enough I now have a ! (error code 43) by my GTX 780 on device manager. I've tried messing with driver updates and it's sporadically removed the ! from device manager but the second screen never came back and the ! is back on the device manager. GPU-Z also says 0MB for memory size and unknown bandwith.

The combination of the GPU-Z data and the error code suggest to me the GPU is finished, but I'm not a tech wizz, so could someone confirm?
What I don't understand is why one of my screens is working despite both being connected to my GPU (one via HDMI and one via HDMI to DVI)

Thanks!

 

[rgd1101]

full system spec? include brand and model of the psu

 

[Cal9099]

full system spec? include brand and model of the psu

Edited my specs into OP