I've recently built a new computer, but a few problems have been plaguing what has otherwise been a good experience. First, my computer specifications:
 

• Motherboard: ASUS Z87-A
• PSU: EVGA Supernova NEX750B
• CPU: Intel Core i5 4670k 3.4 GHz Quad-Core Processor 
• RAM: Corsair Vengeance 8GB Dual-Channel DDR3-1,600
• GPU: Zotac GTX 780 AMP Edition OC 3GB 
• HDD: Western Digital Caviar Blue 1TB, 7200RPM, 16MB of Cache
• Sound Card: Creative Sound Blaster Z 
• Operating System: Windows 8.1

 
When my computer would render games with FPS of 70 or higher, I'd hear a coil whine, which would get much worse the higher the FPS. The PSU I had purchased before the EVGA model was a Corsair CX750W, and it had the exact same problem. Thinking it must be the PSU, I exchanged it for the aforementioned EVGA model. Same problem, if not worse, now. After contacting Zotac, they had me run through some tests, including the 3DMark 2013 benchmark, and that's where I ran into more trouble. The first demo would always shutdown my computer at around the same point. I submitted my GPU for RMA, as Zotac recommended, but, after replacing the GPU with a GTX 460 I had leftover from my last computer, I ran the same 3DMark benchmark and it would still crash on the first demo. Sure, there wasn't any coil whine in games running above 60 FPS, but it's making me wonder if, after all this time, I had two faulty PSUs or if something else entirely is at fault. Otherwise, games perform as expected, the computer is stable, and I wouldn't know there was a problem if it weren't for the coil whine and the 3DMark demo always crashing.
 
I've run Memtest86 and Prime95 for about eight hours each with no errors or crashes. GPU temperatures never exceed 70 C and CPU temperatures peaked at 61 C under Prime95's blend test. Any ideas for what I should do before seeking yet another RMA?

I seem to recall this issue coming up with someone else, but don't remember if they ever figured it out or not.  Have you tried uninstalling and reinstalling 3DMark?  The first demo if I recall is Ice Storm and is really made for low end or mobile systems and really is not useful for anything on higher end systems.  Have you tried the other two demos, Cloud Gate and Firestrike?  If so, did they work okay?
 
Coil whine can be caused by lower quality PSUs, but sometimes it is just because of the card itself.  Can't specifically speak on the Zotac cards, but there has been a bit of coil whine problems with the 780s and 780Tis with EVGA.  Sometimes it will go away or reduce once the card gets burned in.  As you noticed, it is worst when the FPS is high and the card is not really working very high.  Best thing to limit the coil whine is to use vsync, or framerate target to limit the FPS to more reasonable numbers.
 
I would try other benchmarks such as Unigine Heaven or Valley and see if those perform okay.  If those run fine and don't have any issues with other games, I wouldn't worry to much about the one silly benchmark.

Ice storm demo causes your whole PC to shutdown but all other tests & benchmarks don't. Very odd. Have you tried downclocking the video card to -105 on both the core and memory using precision x and rerunning the demo? Does it still crash? What about after you restart your computer still crashing?

Oxford Comma
To clarify, my GTX 780 has been shipped off for replacement, so the GPU I've been using in these recent tests is an EVGA GTX 460 1GB that has had its core clock factory "superclocked" to 763Mhz and its memory clock to 1900Mhz. Do you still suggest that I downclock it by 105 for each setting and re-run the Ice Storm demo?

Yes. I would like to know what happens. I have three titans and can run through that demo without any issues.

Oxford Comma
I downclocked my GTX 460 as you requested, and I was able to run the Ice Storm demo three times without a crash. I have to wait for Zotac to ship me a replacement GPU before I can test the GTX 780. 

A card should work at it's default clock speeds in all games & benchmarks without having to downclock the GPU to gain stability. Since your 460 is your backup card I guess we will have to wait to see what happens when you get your GTX 780 from Zotac.

Disabling this option had no effect. Computer still crashed.

Zotac contacted me and said they were unable to replicate any of the problems I had with the GPU. I suppose that means I have had two straight PSUs that I bought which were faulty out of the box. This is straining my patience and credulity.  I expect to receive my GPU back sometime next week.

Update - I read on futuremark forums if HPET is turned off in bios it will crash 3DMark . Had it turned off in bios , turned it back on . Rerun 3DMark with no issues.

Update: I exchanged my EVGA Supernova NEX750B for a Supernova 750G2, and, from what I can tell so far, there's no more whine or buzz and 3DMark was able to finish the initial demo without a hitch. I now must wait for my GTX 780 to be delivered before I can confirm everything is in working order.

After installing my GTX 780 and testing it with 3Dmark and a few games, I can say my problem is resolved. Replacing my PSU for the 750G2 fixed it.