boots up sometims

Hi! I would remove the battery and connect to AC power in order to confirm that the battery is not the issue.

Is it possible that the computer is falling asleep? If so, the sleep light on the front of the machine will be pulsing, and pushing the power button should wake it up. You might want to take a look at the power settings and confirm that it's not set to do something specific at the time that it is going off.

When it turns off, does the light on the AC adapter still show green or amber? I'm wondering if the AC adapter may be flaky. Try twisting it in its socket, and see if the color flickers, which generally means that either the AC adapter is going bad, or the DC-in (the port in the computer) is going bad.