I have just got done building my new pc, and what happens when I turn it on is: all the fans turn on for about 15 seconds but they spin on and off the whole time, the LEDs on my psu do not turn on while they are spinning either, but the only fans that do spin are my CPU fan and my psu fan, the cooler fan won't spin it just moves a little bit but cannot do the full spin, and my graphics card does not spin at all. Here is what I have in my pc:
Make sure that you have connected everything properly, the 4pin 12V on the motherboard, check that you have correctly installed the RAM. I would disconnect everything and connect only the main cable and the 4pin cable to the motherboard (disconnect all case fans) and see what happens.
If the light in your PSU does not turn on it could be that the PSU is faulty. I would try changing the PSU so borrow it from a friend or if you have one lying around. It could also be the motherboards fault since your graphics card does not power up (re-install the graphics card) but as you described it i would put my money on the power supply.