So, before starting the RMA process I want you to try a few things,
 
The first is updating the BIOS on your new ASUS Maximus motherboard, the bios can be found on the ASUS's website and it should be fairly straight forward like downloading a new program.  Make sure you do not turn off the PC while it is updating the BIOS as this would leave the MoBo inoperable.  Despite the MoBo being new doesn't mean it hasn't been sitting in a warehouse for a few years so a BIOS update could help.
 
Second is to test the MoBo with another GPU if you have one, it can be any GPU as long as its PCIe 2.0 or 3.0
 
You said the GPU didn't work in another computer.  This basically suggests that the GPU for whatever reason isn't working so at this point it may be a fair idea to begin the RMA process unless someone has another suggestion for you to try.  The easiest way to begin the RMA process is to call tech-support at  +1.888.881.3842 and request one, they may also have something more for you to try but it should go smoothly and they can help guide you through the process.
 

If your other MoBo worked fine than maybe you should be talking with ASUS or the dealer you bought it from for a replacement/refund.

You could RMA the card again and I would highly encourage you to try the card you get from RMA in your friends PC first. If it works there than try it in yours. If it doesn't work in yours and you go back to your friends and it doesn't work than we know that your PC is damaging the card.

I highly doubt that two cards would fail in a row naturally, so I believe your PC/PSU/MoBo damaged the card upon boot.

Again, try it in your friends PC first next time.

I did not think of that. Next time I will do this first.
 
But why weren't my other 2 videocards not destroyed?
I used these to check if the MoBo wasn't broken.

frederiekv
Update:
 
I RMA'ed the faulty videocard and got a new one.
After installing it I got the same faults on the motherboard. Again the motherboard refuses to boot, no POST to be seen, no access to the BIOS (MoBo doesn't reach that point). Measured voltages: 12V where they should be (so no shorts on the card).
After much doubt I reseated the CPU: no change.
I tried 2 different videocards in the MoBo (HD5850 (PCIE2.0) and HD7950 (PCIE 3.0)): MoBo boots and I have video from the videocards. So I believe the MoBo is working fine.
Then tried the new videocard in my old setup: no boot. Went to my friend to check and I got the same results: no screen nor boot.
 
Am I doing something stupid? Or do I have a case of Murphy's law? Two brand new cards refusing to work on my new setup.
Thinking of changing to another brand of videocards.

Sounds to me to really be a faulty motherboard, this is I believe the 4th or 5th Asus Maximus VII Hero that have problems with the Maxell GPU and AMD GPU seem to work fine.
On your Murphy's Law, Static Electric Charges, what are you wearing to prevent this Law?
My Friends Computer only helps us if you can tell us what it is and also is it updated and so on.
For one is the friends computer an AMD CPU Based motherboard? Is it Older than 4 or 5 years old?
Was the card installed in the Slot next to the CPU?
Did you plug in both PCIe Power Cables on the Video Card?
Can you Post into the Bios with the GTX 980 Card?
Did you Disable the intergraded Video card in the Bios
If your Bios has Multi GPU Support did you disable it in the Bios?
Was  the Power Cable unplugged on the computer before you stated install the cards?
What was the OS you are using?

Something else you could try is: with your 5850 or 7850 in the primary PCIe slot put the 980 in the secondary slot and see if it's recognized by device manager. If it is recognized it may be an incompatibility between the mobo bios with the GPUs bios.

 some answers to previous questions

bcavnaugh
Static discharge: not that much protection here (grabbing radiator hinges to ground me somewhat).
My friends PC is 4 years old, intel based.
Card installed next to CPU, all powercables installed. Also no access to BIOS (MoBo doesn't boot, hangs somewhere as every other MoBo at my disposal).
His PC has no internal video, all cables unplugged. OS is Win7 but as before we did not get into Windows.

wmmills
No displayport used, my old screen only accepts VGA (I am using a DVI-VGA adpater).
My current screen is only DVI. No displayport available, HDMI I could try on my TV set.

AlexisRO
Installed my HD5850 in the first PCIE slot (also connected screen to this one) and the GTX980 in the second.
MoBo booted and I got into Windows (no AMD nor NVIDIA drivers installed yet otherwise these would also fight).
GPU-Z shows no BIOS version, no GPU clock and no memory clock.
Is GPU-Z accurate? No clock frequency or BIOS. Something is working against each other.
I am going to ticket EVGA maybe they seen this before.
 
Gigadeath22
I cleared the CMOS on my first one but I will try this tonight on my new one

stalinx20
Frederiekv, send your Asus mobo back, and get an EVGA one. I'm only saying that because i have seen too many people have issues with EVGA GPU's while using an Asus mobo. Sounds like these companies are trying to make they're stuff proprietary. I could be wrong...but it's still a theory i'll hold onto. Call me crazy...
 
It's just a thought. If you prefer Asus mobo's then give it another try. Perhaps RMA the mobo and get a replacement.

He also could get an ASUS GTX 980 Graphics Cards and test with one of their own.
Two good things can come from this.
One if it works then you may be correct.
Two if it does not work then we all know that ASUS is the one causing all the issues with the Maxwell GPUs and not EVGA.