Final answer:
If the CPU cooler is incorrectly installed, the system will likely start to boot but then suddenly shut down to prevent the processor from overheating.
Step-by-step explanation:
If a processor is correctly installed but the cooler is incorrectly installed, the most likely result is that the boot process begins, but the system suddenly turns off after a short period. This happens because the processor will start to overheat due to insufficient cooling. When the processor reaches a critical temperature, the system's built-in protection mechanism will shut it down to prevent damage.