Hi there,
this kind of issue can be really frustrating and is one I have experienced for myself in the past.
I guess, as you have tried everything else the best option would be checking your PSU is delivering enough power. In the User's Manual for the GA-770T-USB3, Gigabyte actually recommend a PSU of at least 500 Watts and although your 450 Watt my seem adequate this could possibly be the root cause of your problems. If possible try swapping it for another PSU to see if it is as simple as that.
The other thing that springs to mind is have you manually set the RAM Timings and Voltage or have you left them at the System Default settings? I had all kinds of problems when I tried to set my Corsair RAM to their stated ratings and eventually discovered that it was better to leave them set at the system defaults. They should have been able to run at 8,8,8,24 but preferred running at 9,9,9,24.