If your mobo has an 8-pin connector, you can use either a 4-pin or 8-pin connection with no real difference in performance. If you are OCing your system you should use 8-pins, otherwise, it really doesn't matter in most cases.
Will the system boot with the old PSU?
Also, with the new PSU, you can try this. With only the PSU attached to the mobo and the GPU (if required) and NO other devices, see if the system will boot to the point where you can enter the BIOS.
That would indicate a short or bad power connector.
What make and model of PSU is your new one and is it a modular PSU?