Can a malware power on a computer?

I've just downloaded and executed a piece of malware on my computer.

I don't have much time right now, so I just powered it off (turned it off via the Start menu), hoping that it won't be able to steal any data or do malicious activities until I can nuke it from orbit.

• Is it enough to prevent the malware to continue to carry out maliciousactivities?
• Can the malware power on my computer?
• Should I also unplug it and remove its battery?