Can you cause a CPU failure by puting in a faulty motherboard?

I have two machines based on Gigabyte m/bs

1 = GA-81945GMF running a Skt775 P4 (531) 3.0Ghz - Was fully working
2 = GA 81945GMH-RH Skt775 built but no processor.

I took the CPU out of working machine and placed in new build to test.

Powered up No Post on screen. Fans on PSU, CPU and case (m/b linked) all start on power up. Left on for no more than 1 minute, given no post.

Took CPU out and put back in previously working machine. Powered up but no post but fans work and CPU Heatsink gets hot implying CPU has power.

Machine 2 motherboard is new as are all other parts.

If CPU heatsink in machine 2 not properly seated could I blow CPU (Don't P4 CPU's have thermal safety cuts outs.)

Any ideas / thoughts anyone?

Thanks

David