Probably not.
Information to include in the answer: Computers work because of an intricate system of components that need each other to function. It is possible, though unlikely, for a computer to turn on without its CPU because it would require all of the other components to still functioning properly. This chance is all but eliminated when the motherboard goes down as well- this would require at least 99% or 100% of other major components also intact and working correctly before it could happen!
If you take out the CPU, your computer won’t work. But if you remove even one component-whether it’s your keyboard mouse, monitor, DVD drive-and put in another one instead (say an Xbox), your PC should power up just fine.