Well it will never turn on with the plug pulled out will it?
It may be a broken set - a blown fuse - a bad wall socket - a broken remote control - TV sets usually have a manual on and off control - have you tried both methods? Have you eliminated the fuse and the socket?
It may need to visit the TV doctor. The fact that you didn't mention the make or model has not prevented me from trying to help you.
Good luck...
August 2015