How I test if my cpu is damage

Between motherboard and CPU usually the Board!

completely dead or not booting up?

The fans and cpu(apperently) try to start booting up, but rapidly turn off. With a freind we troubleshoot everything except the MB & CPU. He said the unique way is put a MB and try. A Motherboard and try.
He tell me the only it to try those two components.

In that case it is the motherboard.
If your system trying to start for atleast 5sec,remove your cpu fan and touch the cpu and turn it on.if it heats up,cpu is fine.
To check mobo,remove any pci cards you have and ram,make sure you have inbuilt speaker ot connected speaker for your mobo.after removing ram try to start if beep sound hears your mobo may not hardware problem.(google for more)

do you tried to update bios?

i do not have inbuilt speaker(I do not see it) but connected the external speakers from MOBO not beep sound hear. The CPU do not heats up too. I left the system for minutes, turning o and of and touch the CPU it not heat up.

Has to be motherboard speaker for beep codes, external does not work on BIOS.