If it was the PSU it wouldn't boot at all. If it will not post at all, my guess is your motherboard is dead. Try getting into the BIOS. If you can't, then yeah its the motherboard.
do you have other display ports and or cables to test if its just a problem with the port you have been using? (Like if the dvi port is dead, you use another dvi and then get a signal)
I worked as a staples Easy Tech for 2 years, and in that time if a computer did not post then it was usually something like the ram, or mobo. Seeing as how you just got a replacement mobo, trying using only 1 of your ram sticks at a time, and see if it will boot with either.
Bc it does sound like we have ruled out all the other possibilities. You couldnt even take it to a bestbuy or staples bc they dont handle things that wont even post.
Basically, sometimes that can happen. I remember one time someone brought in a laptop and it booted and then it just died right there.
But it will be either:
mobo
power supply
RAM
cpu (very very unlikely)
Usually in that order. And it could've been damaged in shipping.
To test for power supply, simply jump it and see if it will not shut down immediately. To test for ram, plug into another computer and run memtest86(will also test cpu).
I'm sorry, but this is the best I can do. Without beep codes, or any sign of post, theres not much else.