as far as the RAM is concerned... yeah it is possible that either a bad stick or badly seated stick could cause this.... BUT normally you should see at least the video bios kicking in first followed a POST error indicating an error with the RAM... so I don't think it'd be the RAM but certainly it's not something I would rule out at this point. If you have spare memory it would be worth pulling out all sticks in the new pc and putting one stick in that is known to work - if it doesn't work first time try another slot... maybe the slot you have the stick in at the moment is faulty.

Swapping over the CPU's is a bit more drastic... and obviously carries certain higher risks if you don't seat the CPU properly - but being as you have built more than a couple of PC's I guess you're going to be reasonably comfortable with doing that. I'd try this one last.

Still at least you know it's not the vid card!