Hi,
in my opinion the PSU (500W) is actually quite small for the specs you've given. I'd try a bigger one, at least 650W or even more. Borrow one if possible before you buy and confirm if it solves the problem.
Why? Even *if* the PSU was coping with the load for some time, it was probably on the edge. Components might have suffered from excessive loads over a lng tie and therefore slowly burned out. Especially if something changed in your environment, like having higher ambient temperatures than before that might have triggered the final failure. Also consider testing with onboard graphics/another graphics card. You might have a problem there.
I had a similar problem in the field, with a similar hardware setup. Here the motherboard had developed a short for an (unfortunately) unknown reason, but the system was showing similar symptoms. I say similar because it came on, ran for one or two seconds and then shut itself off. That happened some short time after a high performance graphics card had been plugged in...
Just coming to my mind, I had another one, ASUS MoBo, that actually did exactly the same yours does. After several days of trying different BIOS settings and diagnostic procedures and starting to work a couple of times it finally never stopped looping/power cycling. In the end even in this case (it was a P68 chipset with an i7 2700K CPU) the MoBo turned out to be faulty. We replaced with a Gigabyte MoBo (no advert, just to let you know the changes...)with not exactly the same chipset (it was Z68 instead), but worked immediately without any further changes.