Hi,
I setup to first time burn bootloader into an Atmega168 10PU, and I failed 
Could it be for the standard chip coming with my original Arduino board was a 20PU?
The 20PU is rated to run at 20MHz while the 10PU is rated for 10MHz max. The standard Arduino bootloader is designed for 16MHz. Trying to load it on a 10PU could cause a problem. I would try loading the lilypad bootloader that is designed to run at 8MHz. If that fails, then you ruled out the bootloader.
Thank you for the clear answer!