I'm hardly an expert, but here's a take. Keep in mind that "won't turn on" is one of the most difficult problems to diagnose.
Is the heatsink properly installed on the cpu? Is the heatsink new out of the box and installed for the first time? If not, did you use thermal grease?
Second, are both the 24-pin and 8-pin power cables connected to the motherboard? Are any of the fans at least starting to spin?
I realize this is basic stuff, we just need to rule out the obvious suspects.
Also, you might try using only one stick of RAM in different slots.
That's off the top of my head. If everything is installed correctly, its either motherboard or CPU. If you have the other i7-860 system available, switch out its CPU with the new one. If it works, that will definitively rule it out as the culprit.