Best couple of suggestions I can make would be first remove the MB and do a barebones set-up on a piece of cardboard (make sure it is larger than the MB) only connect the PSU, the GFX and only insert 1 stick of Ram.
You will then need to short out the 2 power on pins on the MB header to get the PSU to activate, you can use a small flat bladed screwdriver or a paper clip bent into a U shape, this is perfectly safe if you do not touch anything else, the idea is to see if we can get a BIOS screen if you do you can then add one component at a time until you find the problem component, you must power down and remove the power cord from the wall before adding a component, second suggestion try re-seating the CPU, to do this you will need some TIM (thermal interface material) such as Arctic Silver 5, let the computer run for a few moments to warm up and soften the existing paste between the CPU and HS as this will help to make sure they separate easily as sometimes removing the HS and CPU fan can pull the processor from the socket, clean and prepare the CPU and then apply a fresh amount of TIM, too much is as bad as too little so only use the correct amount.
NB: For testing purposes use the original PSU first because if it is working correctly you can return the newly purchased one, also this is a long shot but worth a try, before doing any of the above try clearing the CMOS by removing the silver CR2032 battery on the MB, this will restore the factory default settings, if it works you will need to go into the BIOS and reset the time and date then save and exit. Thanks to rshaffer61 for the battery image.