Hey there
Is it shutting down by itself?
If it shuts down by it's self, does it power down immediately(+-2seconds or less) or does it say, Windows is now shutting down?
If it shuts down in less then +-2, there may be a hardware issue. Take it to where you bought it to get checked out.
If it accualy says, Windows is now shutting down, then the most likley casue is that you have a virus. (Probably the Brotok Virus). It doesn't do that much harm.
Install a anti virus. eMachines have McAfee trail version installed. Make sure it's activated and not expired.
BE CAREFULL AFTER installing a anti virus. If it detects viruses, readup about them online. If you have a file infecting virus your applications will be deleted from your PC. Your anti virus should have a home page online. They should have removal instuctions there..
Hope this help.
Cheers
Grant