First i would remove every component from motherboard even the CPU and start up the motherboard with a CPU fan to check if the motherboard is fine, then i would put CPU w/ heatsink and one ram and see if it works if it has onboard GPU if not plug GPU then, if it works, plug rest back one by one and if everything passes then it seems fine, if you get stuck with no picture and etc. then that component probably died.
Which new psu is it?
Also post system specs.