I searched all over Google for the answers for this and most of them read that the PSU is at fault, but I did the paper clip test where you connect the green wire to one of the black wires (ref: http://aphnetworks.com/lounge/turn_on_psu_without_motherboard_the_paperclip_trick) and the fan spins.
So I thought my mobo was having problems, so I returned it, got a new one and I get the exact same problem. So I don't think it's the mobo at fault.
Update
I placed the motherboard over an anti-static grey clear bag (the one that you get for free when you buy a motherboard) just in case the case was shorting the motherboard, unplugged everything except for the RAM and CPU, and the same thing happens – it turns on for a second (I can see the fan spin) and then shuts down immediately. Keyboard and screen are not even attached.
Update 2
I found the solution to my problem. I posted it below.
Best Answer
A bit hard to diagnose without seeing, however if someone came to me with this problem I would do the following.
Just to rule out any other sort of problem with the PSU, can you try turning on your PC with only the power cable, screen and keyboard connected and see if you can get into the BIOS, if you can, it means that either your PSU has insufficient output for the amount of hardware you have, or a piece of hardware is bad.
If it is the insufficient power in the PSU, try buying a different higher rated one.
If a piece of hardware is bad, try plugging in components one at a time until it breaks again.