Question

A computer that starts up and then shuts off at various stages of the boot, but eventually boots normally is most likely having an issue with

Answer 1

The computer is most likely having an issue with the electrical system. First, I would unplug the PC - hold the power button for 10 seconds - plug the PC back in - wait 30 seconds - press the power button back on. If this doesn't work then check the PSU for voltage issues, and then check the motherboard for issues.