Problem with power? 3ds works only with cable.

Hi, sorry for my English but i have problem. I bought nintendo 3ds from shop where was demonstration. When i put in cable console start working. But when i put out cable it shut down. First i think that was battery so i decided to buy new one. I replace battery unit but the problem still the same. My question is whats wrong with device? Meyby power on button have issue? But when i try to turn off when cable is in it show me "turn of"? When i chose turn of it going to restart. Help please, in my country we dont have nintendo service.