A very common thing when upgrading the CPU is that the power supply is pushed over the limit, especially if it is a cheaper model that was already at the edge before. I note that you did not mention the wattage or maker of your psu. If this is because you did not consider it worth thinking about, maybe this could be a possible thing to check out?
I am surprised nobody has suggested this.
Those reboots sure sound like my AMD upgrade frustrations, which were cured by a decent branded power supply to replace the no-name one I had that came with the $40 case I purchased... (a lesson learned there, I can tell you!)
You could try reducing the load somewhat by only having a minimal hardware config - onboard graphics (if available) rather than GFX card, hard drive only, (my psu used to quit as the DVD drive spun up) and see if she boots OK, in that case your PSU would definitely be implicated, but even if such a test did not remove the reboots, I might still suspect the PSU. maybe some data about it would be a useful thing to post?