If you've reached the point where HR is actively trying to find a way to fire you, that probably means you royally pissed off someone in a position of power, an

If you've reached the point where HR is actively trying to find a way to fire you, that probably means you royally pissed off someone in a position of power, and your use of company equipment for personal emails is the least of your problems. If you didn't do that they would certainly find something else to fire you for.