Guys I have the exact same issue. Bought a GTX980 last year around October or November, along with a COMPLETELY new build, new parts everything. All quality parts. And a Gigabyte Z97 FORCE motherboard. No issues whatsoever except for the GTX980 that will sometimes black out my entire monitor by not sending a signal to the displayport when getting to the Windows 7 login screen. (this is well documented GTX980 issue), other than that it worked perfectly I get good benchmarks and everything. Not overclocking and all temps are well below normal.
Then early this year, about 3 or four months after my initial build, I notice this very low level "buzzing" sound coming out of the PSU. I am sure it is the PSU. It took me a long time to isolate the exact source of the low level buzzing and it was driving me insane. Sometimes the buzzing would be louder, other times more quiet,. other times it would completely go away on its own. It was intermittent, and with no solid pattern other than the fact that I noticed more often than not, it would usually typically be completely silent when I first boot up the computer, then after the computer was used for an hour or so, it will gradually start the buzzing noise getting louder until it reached a peak. This happens even when I just idle the machine or surf the web, nothing with me loading the CPU too hard or playing games etc. After a few more hours, sometimes the sound goes away, then only to come back later.
As this progressed I noticed that it would happen sooner. Eventually it got to the point that it would only be silent for the first five minutes, then after that shortly after bootup it will start manifesting that noise again. .
I thought about everything from the PSU fan needing to get more lube, to some capacitor going bad, etc... Eventually I just got feed up and went out and purchased another brand new PSU (AX860) to replace the Corsair 850 and immediately after swapping the PSU the noise was gone for good and never came bad. So I attributed it to the PSU and never gave it another thought.
Now, less than a few months after that, I recently started to notice the same buzzing noise coming back, this time on my new PSU! This can't be a coincidence. I don't operate in a dusty environment it is very cool, clean, this can't be something to do with a broken fan or needing more lube. I don't have any performance issues with the computer, specs and benchmarks are as they always were. I am not infected with a virus, to be sure I even low level reformatted my computer, got a new SSD to make sure there wasn't a firmware infection, and switched to a new BIOS (my motherboard has a switch that flips to a backup/dual bios) to make sure my motherboard wasn't somehow compromised.
I can't imagine why. I'm using a quality Monster surge protector and also running an APC Line-R rated at 1200+; I am feeding it the best quality power possible.
My speculation is that like the Displayport /dark monitor /lost of signal at login screen issue that is the result of GTX980; I think my graphics card is actually the culprit that causes for whatever reason(s) my PSUs (two of them now) to develop a buzzing over time.
I'm not sure what affects this has long term on physical use and performance, if any, but the sound is annoying and buzzing is bothering me. I built an otherwise very quiet system and this is irritating.