Try the 970 in your rig, and I would also have your friend try the 1080 in his - if he's willing.  Then you would know for sure if its the card or not.

how many watts is the PSU?
 
edit: nvm i saw it on your sig
 
 

Sounds like one or more of the VRM's has shorted out causing your power supply to shutdown (ie. crowbar) due to high current.  Most power supplies these days have over-current protection, you should NOT install the card in any other machines, RMA it back to EVGA.
 
** Edit **
Crowbar circuits are for over voltage protection and usually included in most power supplies as well.  In both cases you usually have to remove the AC mains either by shutting off a physical switch or disconnecting the power cord in order to reset the circuit.  
 

IchigoSoulReaper

hapkiman
Try the 970 in your rig, and I would also have your friend try the 1080 in his - if he's willing.  Then you would know for sure if its the card or not.

Yup I just did and my computer works with his 970 but his computer won't with my 1080. When the 1080 is in, the LEDs flash once and then the computer won't turn on. It's like it activates a surge protector or something. So it's definitely my GPU.
 
Any solutions or do I need to send it back to EVGA?

Time for an RMA. You tested it in a different computer and had the same error. Your system functions with a known good GPU. Just cite this thread when you request an RMA. Personally, If you can, I'd do it by phone. It's quicker and they are there 24/7.
 

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• Tel: +1.714.528.4500
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Ok... i have a similar problem with my EVGA 1080 hybrid ftw gaming. I was playing for honor and while playing my card went very loud. I turned the computer off. I waited like 5 minutes and was not able to turn on my pc any more.
 
The LEDs from my mainboard and my AOI Watercooling flashes one second when pressing the power button but the pc wont turn on. I bought the card this year in may 2018 my average temperatures were 30° in idle and while playing max. 55°.
 
I´ve tried to turn on the pc with my old EVGA 980 from my working pc to be sure its not the board or the boards pcie slot and like i allready was afraid, the pc turned on.
 
To be 100% safe i went to a local pc store and they checked every other component of my pc except the 1080. They confirmed that everything is allright. I am from Germany and im reading a lot about bad support of EVGA in Europe.
 
I now need a support ticket id that i will get after a support tech responds to my case and after that i can start the official RMA. I hope EVGA suprizes me with good service like im used before and that bad support talk is just rumors... 
 
Anyways i was expecting a better quality product for that price.. I will also post back here just to share my experience with the community.
 
My english is not the best i know.. sorry for that. 
 
Cheers, Callud
 
My System Specs:
 
PSU: Cooler Master RS-600-ACAB-B1 600 Watt 
Motherboard: ROG STRIX Z370-F GAMING
CPU: Intel Core i7-8700 (Coffee Lake) Socket 1151
Cooler: Corsair H115i Pro RGB
GPU: EVGA GeForce GTX 1080 FTW Hybrid Gaming
RAM: G.Skill RipJaws V Series rot, DDR4-2666, CL15 - 16 GB Dual-Kit
Storage: Samsung SSD 850 EVO 500GB
Monitor: ROG Swift PG279Q (WQHD)