Do you have the power cord plugged into the DC IN port of the camera? (Please note that the camera has 2 mini usb plugs, one is a USB port on the side, while the other is the DC IN port at the top of the base.) You are looking for the DC IN port.
The camera should turn on automatically once it receives power to the DC IN port. If the power cord is plugged into the USB port on the side, it may cause the camera to shut off after 8/10 seconds.
Please make sure to to let the camera charge for a few hours. Once plugged into the DC IN port the camera will automatically power up and be on until the power is cut.