My camera won't stay on..

Ok. so everytime that I turn on my camera to take a picture it shuts off after like 2 seconds. I put in new batterys and it still does the same thing. Some times when it actually stays on, I'll review my pictures and the screen goes black, and it turns off again. When it shuts off, the lens, (zoom in and out thing) stays out. I thought maybe it might be my memory card?? I bought it probably two years ago.