My computer switches on its own in the night . Is my computer hacked

Could be. Is it connected to the internet by a cable or DSL connection? One surefire way is to unplug the machine and that eliminates anything and everything. Also get a good web security program and anti virus program. Can't be too careful these days. Be sure you don't have any kind of remote accessible help activated either.

Make sure you have a good firewall installed on your system. That sounds like a zombie pc. A zombie computer is inffected wqith a trojan,which is used by the hacker,and use your pc to spread malware,spyware or simply to use it in a "dos" atack.
DOS= denial of service

Dude, if you computer is shutdown, then there is no power flowing into it, and it cannot turn on by itself, since you need a program to do that, and programs run off of Operating Systems, and if your computer is off, your Operating System isn't loaded, and it cannot turn itself on. Someone is either turning it on at night, or someone messed with the hardware to make it turn on.