Power supply

Hello
Here is my problem. My computer will turn on and off all byitself. It wont even boot up all the way before it turns back off. it will do this aslong as i have it plugged in. When it finally stops turning on byitself and i try to turn it on. It wont do anything. no lights flash or anything. If i dissconecct the power cord and reconnect it it will turn on only for a few seconds then turn off. I went to the local computer store and asked them the question. They said it could be the power supply. i was wondering what you guys think it could be. If it is the pwer supply would it be cheapers to get its fixed or buy a new one.