do you know for certain if the corsair psu works? if it does, i would try it with that psu. If the system still doesnt start, the psu isnt the problem. Im pretty sure 600W is enough. But first, here's a checklist of things i would do, im not sure if you've done them yet or not. if you have you dont need to again:
1. make sure the case standoffs are not shorting the mb, make sure all power connectors are plugged in
2. try booting without the gpu plugged in, with the monitor connected to the motherboard's igpu. if nothing works, could be psu, mb, cpu
3. check ram: only put in 1 stick, if it doesnt work try the other stick, if that doesnt work try a different slot. repeat. if nothing works, the mb could be DOA, or it could be cpu, gpu(if not removed, which it should be for this step). continue with list.
4. check psu: try replacing with a working psu with enough wattage to start, first without the gpu and then with the gpu.
dirst try these things, if anyone else has a troubleshooting idea feel free to add to my list by replying