I bought custom parts to build a new gaming desktop. I've plugged everything in where its supposed to, (I'm not that advanced in computers) and the computer will turn on (the CPU fan does not turn on right away, it goes on after about 5 seconds at a high speed, then slows down). After the CPU fan slows down, 1 second later the entire computer shuts off. I think this might be a CPU overheating issue, but I'm not too sure. Again I know very little about computer parts.
Intel Core i5-3470 Quad Core
Corsair Vengeance 8GB (2, 4 GB) RAM
WD Blue 1 TB Hard Drive
Samsung DVD-Writer Optical Drives
Cooler Master HAF 912 (Case)
Cooler Master GX - 650W 80 PLUS Bronze PSU
GeForce GTX 660ti 2048mb GPU
Gigabyte GA-Z68MA-D2H-B3 Mobo
It's not overheating since the CPU wouldn't get that hot that quickly. I do, however, notice that you have a third-gen CPU (i5-3470) with a 6-series motherboard (Z68 chipset). Z68 boards were made for 2nd gen but can support 3rd gen chips with an updated BIOS. What I suspect is that your board might not have an up-to-date BIOS which supports the newer CPU model.
You can update the BIOS, but you'll need an older CPU supported by the currently installed BIOS to do this.