[SOLVED] 2 laptops and 2 CPUs, possible faulty CPU or power issue on MOBO: how to diagnose without causing further damage?

[pnvr8e]

I have 2 laptops:

1. NEC VersaPro VB-B with i5 560m(working, no issues)
2. HP Elitebook 8440p with i7 620m(auto shutdown sometimes even just after turning it on)

Both CPUs are for the same socket. I am not sure if the i7 is faulty or if the 8440p has a power issue on the motherboard.

If you put a faulty cpu in a working motherboard, does the combo damage the motherboard?
If you put a working cpu in an faulty motherboard, does the combo damage the cpu?

I'm looking for a way to narrow down the issue and I'm left with just the cpu or mobo to blame. All other parts of the 8440 were removed and the shutdowns persisted. I'd like to find out which is broken without adding further damage to the troubleshooting components.

 

[Koekieezz]

If you put a faulty cpu in a working motherboard, does the combo damage the motherboard?
If you put a working cpu in an faulty motherboard, does the combo damage the cpu?

Faulty CPU on Mobo: depends on which faulty, not every faulty does cause damage, and if a cpu is totally broken, it wont even boot.
Faulty Mobo with CPU: it could damage the motherboard as i did ever experience it before.