Thanks for the update.
A possible problem is,
The GPU power connection required, 1 x 8 pin and 1 x 6 pin and recommends a 500w PSU.
Your PSU only has 1 x 6+2 = 8 pin. Without the 2nd power connection the GPU will not work, or, if you are using a Molex to PCI-E converter, you may be stressing the 12V rail a little too much, that would cause a shutdown.
Your RAM is 6.25V, the Default for you CPU is 1.5V. If the UEFI (replaces the older style BIOS) has not detected the RAM correctly, you will need to engage the correct XMP Profile.
To simplify troubleshooting I suggest you do a bare bones test setup as follows.
When working on the computer, always switch off the PSU and take anti static measures by briefly touching a bare unpainted part of the case.
Remove the GPU and any other add on cards including the wifi module.
Remove the RAM.
Disconnect all cables including the monitor.
Remove the MB and place it on the MB box, close to the side of the case.
Connect the 24v and auxiliary 12v cable to the MB, (two cables) insure the CPU fan is plugged into the CPU fan header on the MB.
Connect a keyboad and mouse.
Connect the monitor, use a VGA or DVI MB integrated video socket, swith it on, you should get a No Signal displayed.
Switch on the PSU,
On the MB front panel header, with a small bladed screwdriver, briefly short out the power on pins.
The PSU and CPU fans should start and keep going. The LEDS on the keyboard should flash once, If you have a MB speaker fitted, you will hear a beep code, you should get some message displayed on the monitor.
Please post back the results.
MB Manual, > ftp://184.108.40.206/manual/H97M-ITXac.pdf