Mainboard shuts itself off after half a second or so
Solution 1:
It could be a hardware failure of your motherboard. Look for capacitors with bulging tops or foam leaking out of them. If the power supply detects a short circuit it will behave just like you where describing. Also there are some other self tests the CPU does before it even shows the POST screen, and it it fails those it will do what you describe too.
After double checking that you have correctly connected all of the cables (the large power connector and the 4 pin connector, also check to see if your GPU needs it's own power connector) I would try a different motherboard with the components from your PC (CPU, RAM, GPU, PSU) and if it works that you need to replace the motherboard.
There is a 2nd power connector for your motherboard, from your comments it seems that you did not connect it. JPWR2
in the below image
Does it work if you connect that cable?
Solution 2:
It could be overheating.
I had a machine which behaved similarly (after being dropped about 6 inches unto carpet). It would sometimes last a few seconds (possibly as many as 5 or 6), but other times it would cut out a lot quicker (ie less than a second).
The problem turned out to be with the heat sink which must not have been making good contact with the processor, because after re-attaching it with some thermal transfer/glue, the problem went away.
Note, there was no visual indication of this, and the heatsink was screwed to the motherboard (not just glued to the processor) and it did not appear to be loose.
I wasn't the one who fixed it and to be honest, I thought my friend who did this was wasting his time, but thankfully he didn't take any notice of my opinion.