dimopeev01 :
Well I checked the PSU, the fan is still spinning and according do the video by Corsair this should mean it is still functioning properly.
This, is so far from correct that I'm once again not sure how Corsair ever manages to live down some of the things it does and says. It's a good thing they have a lot of good power supplies (And a history of really bad ones too), or I'd simply go full on anti-Corsair when it comes to power supplies.
In any case, there are PLENTY of ways the fan on a PSU can still work and the unit be failing or have already failed entirely in one way or another.
If you have a multimeter or can borrow/buy one, even a cheap model, that would be a good INITIAL way to test the PSU. As follows.
https://www.youtube.com/watch?v=ac7YMUcMjbw
Briefly, I'll just say that I've seen plenty of systems that failed to boot, or power on, or just had so many different problems it was hard to just pick one out and go from there, that had functional fan operation but had like 8v on the 12v rail, or 11.4v, and anything below 11.5v is likely going to cause something to either not work or work poorly. There are probably about twenty other similar types of problems I could list, but I'll stop there because it really doesn't matter HOW it's not working, if it's not working. Normally we'd try to look at voltages using a utility on the desktop first, and then go to the multimeter, but since you can't even boot, that's where I'd start if you can't simply swap in a known good unit with plenty of capacity to rule out the PSU.
As far as motherboards go, before I go that far I think I'd pull the CPU cooler and make sure it's not packed with dust and hair, etc., in the heatsink. Also, make sure the thermal paste hasn't dried out. You'll need to have new thermal paste to apply in order to reinstall it.
Also, verify that the CPU cooler fan is even spinning.
As for motherboards, any of these should be satisfactory.
These are the boards that I'd recommend as being suitable for use with that FX 6 core CPU. The closer to the top of the list, the better. All of them are members of either the 990fx, 990x or 970 chipsets. This is important because there are other, incompatible chipsets that use the same naming/series schemes as many of these models, but they will not be compatible as they will be different chipsets.
GA-990FXA-UD7
Extreme6
Extreme9
Fatal1ty 990FX Professional
Crosshair V Formula-Z
Sabertooth 990FX R2.0
GA-99FXA-UD5
MSI GD80V2
M5A99FX PRO R2.0
GA-99FXA-UD3
MSI GD65V2
990FX Killer
Extreme4
M5A99X EVO (R2.0 as well)
GA-990XA-UD3
990XA-GD55
GA-970A-UD3P
M5A97 or EVO or PRO (R.2 as well)
GA-970A-UD3
970 GAMING
970A SLI Krait (USB 3.1 supported)
Extreme3
970 Extreme3
M5A97 LE R2.0
970 Pro3 (R2.0 as well)
GA-970A-DS3P
GA-970A-DS3
GA-970A-D3P