Then I would suggest that you REMOVE ALL of the hardware from the system that works, and use THAT power supply and memory with each of the boards that won't seem to work until you figure out which component is causing you problems. And for the record, IF you are using ANY cables, at ALL, with ANY of these power supplies, that did not COME with THAT power supply, then that is a problem and you've probably wrecked something. Not saying you have done that, but I see people on here do it ALL THE TIME and wonder why their crap doesn't work. So if you are using ANY cables that didn't come with a given unit, don't do that.
What are the specs of the system that the 3600 and 5500 DO work in? What is THAT board model, memory kit model, power supply model, etc? And for these others, I'm assuming you have NO other hardware connected aside from the graphics card. No drives, nothing. Just board, CPU, one stick of memory and power supply. Nothing else. Until you get it to POST. It's really very simple. If both CPUs work with one board, memory and power supply but do NOT work with two other power supplies, two other boards and whatever else, then one of those common denominators must be the problem OR you are forgetting to plug something in either fully or in the right place. Or at all. Can't tell you what you are doing wrong when we are not there to SEE it. You kind of need to put the work in in that regard. So, if your other board works with both CPUs, then try the power supply and memory you are using with that board with the other two boards and see what happens. If nothing, then it has to be something YOU are doing wrong.