Why would a CPU cause issues in one unit and not in another?

[Nocturnal]

I have a laptop that has a P4 with HT CPU. It reboots as soon as it gets passed the BIOS screen. It keeps doing it. I removed said processor and put in a test Celeron D which runs at 533mhz. It boots into Windows properly. It runs, no reboots. I take the processor that is giving me problems and put it into a desktop computer and it boots into Windows and I ran Prime 95 on it just fine. Any ideas?

 

[CCityInstaller]

Does the Celeron operate at the same Vcore as the P4? If it doesn't then it might be possible that the notebook is not supplying enough Vcore to the P4, while the Celeron requires less and its being supplied properly. I am not a huge fan of the P4, so I don't really know much about them. Is is possible that the P4 is tripping some sort of thermal protection in the notebook? I had a similair issue back in the AMD Socket A days where that would happen. I couldn't figure out why the computer would power down after the bios post, and it was due a heatsink that wasn't properly seated.