I have seen similar posts about this, but nothing quite explaining my particular situation. Usually I have no issues powering on, the only time it happens is when I leave the power transformer on that the PC is plugged in to overnight (American living in UK), but if I dont have it on and I go to flip it on (the transformer) first thing in the morning, the PC turns on fine. I don't think the transformer is causing issues itself although I can't be certain. The PC will give a brief sign of light, the fans and LEDs flip on for a split second, and if you press the button again, nothing. The only way I found to fix it is to unplug the 24 pin connector, either unplug the power cables from the GPU or pull it out completely (which has been the recent case), then plug the 24 pin back in and it powers on just fine, then I can plug the GPU back in and it works as it should. From then on, I can turn it off and it will power up normally, and restart normally.
Hardware is as follows:
Motherboard:
Gigabyte GB-970A-D3P
Processor:
AMD FX6300 black edition
Hard Drives:
random 500gb HD
3x Intel 730 240GB series SSD in RAID 0
Graphics card:
Gigabyte GTX970 G1 gaming edition
PSU:
BFG 650W
Hardware is as follows:
Motherboard:
Gigabyte GB-970A-D3P
Processor:
AMD FX6300 black edition
Hard Drives:
random 500gb HD
3x Intel 730 240GB series SSD in RAID 0
Graphics card:
Gigabyte GTX970 G1 gaming edition
PSU:
BFG 650W