But if it's an AMD M'Board you could have a incompatibility between the Video Card & M'Board. That's very common even when the M'Board & Video Card are from the same maker or have the same chip set brand on them.
The PS could be on it's way out so I would suggest that you test it with a Known Good one to see what if anything happens.
The Jumper for the CMOS could be set to clear and not allowing the system to actually start.
The CPU could be fitted the wrong way around and not working at all if it's still capable of running
You could have a faulty HDD or other Optical Drive that is pulling the available power low and preventing the unit starting.
You always could have a faulty M'Board but unless you didn't follow normal Static Control procedures correctly this is unlikely unless it's one of the cheap nasty ones.
The CPU from the Old M'Board may not suit this new M'Board.
The monitor may be faulty. I've been caught by that previously and what made it worse was it was my test monitor that had gone bad.
Disconnect all the unnecessary things and just leave the CPU, Minimum RAM and Video Card in place and see what happens when you try to start the unit. If you get a Video Signal you can them try connecting one unit at a time till it stops working. If that doesn't work you can do 1 of 2 things either try another PS or do as I would normally do pull the M'Board sit it on an Anti Static Surface and plug in a PS then connect up a Mouse Keyboard and monitor and short out the power pins to see if it's going to work before you even attempt to assemble it.
I don't like wasting time on hardware I don't know if it works properly before beginning the assembly so I just fit the bare essentials and power up to see if I get a Video Signal and then set the BIOS to what I need. I then power down and fit the M'Board to a case and then go about setting up the system properly but only after I know that it's working first.
Col