Root Kit malware can do this and much more. However, rootkits are normally used as spyware to gather information from your system without your ever being able to detect that your system is infected. Powering up your system, doing some mischief, and then powering back down would not be useful from a spyware perspective since it doesn't know and would be difficult to predict your computer usage schedule.
A really well written root kit would not be detectable to a system that does not have equally well written anti-malware protection. In your case, the malware has been detected. Consider yourself fortunate. To protect your system from root kit malware :
never, never log in as root user or administrator!! Always use 'sudo' (linux), or 'run as' (Windows) if you need to do something system wide.
Make sure you have a very strong root user (administrator) password, and change this password as often as practical.