Well, you can try putting just the motherboard and power supply in the new case, see if it will turn on. If it does, turn it off at the PSU and add the graphics card, see if it will turn on. Continue in the same manner, adding devices one at a time and testing after each.
If just the motherboard won't power up in the new case, then check and make sure nothing metal is shorting against the motherboard (touching it where it shouldn't). It is also possible (unlikely, but possible) that the power switch is bad out of the box. You can try carefully shorting the pins where it connects with the end of a small flatblade screwdriver to see if it will turn on. Be careful only to touch the correct pins!!!
I've tried using the power switch on my old cpu case( the one my cpu components was in originally) and it also doesn't work. the motherboard and everyone was in the new case but i simply just connected my old cpu case's panel+power button to the motherboard to test it out. i will try the other method as to removing the motherboard completely from the case and see if its shorting out by it touching some sort of metal