I had the same problem with my motherboard. Would not power on, with only a brief flash of light on the PW_SW button on the motherboard. Here is a solution. Warning: The CMOS settings will have to be re-done as they will be wiped out with this process. Disconnect the AC Power cord from the power supply, or it there is a switch on the power supply, then turn it to the off position. Remove the backup battery, and wait a bit. 30 seconds or so should do the trick. Re-insert the battery. Plug in the power cord, or turn the power supply switch back on. Press power on. Boot into CMOS to re-do the settings. If you still have no luck, replace the backup battery and try the above steps again.
I am not sure what causes this, or why the battery has to be removed to fix the problem. Resetting the CMOS does not do the trick. This is my second motherboard this has happened on. The first time I reported the problem to Gigabyte. They told me to RMA the board. When it happened on the 2nd board, I knew there was something not quite right. One final comment. This is now the 2nd time this has happened on my 2nd board, and I did not do anything unusual. Just powered off the system, and the next day it would not power on. Weird.