If you only have the one camera and one card, it's going to be hard to determine which is the problem. As commenters have suggested, the easiest way to troubleshoot such a situation is to:

• try the memory card in another camera
• try another memory card in this camera

With respect to the "control panel light" staying on, I'm not sure what you mean by "control panel light". If you mean the little light that lights up when the camera is accessing the memory card, it could be related to your memory card troubles. If you mean the big color screen on the back of the camera, or the LCD display on top of the camera (that shows shutter speed, aperture, etc), and those are staying on when the camera is in the "off" position, then there is definitely a problem with the camera. The color screen on the back of the camera should be off when the camera is off. The LCD display on top of the camera should be off as well, with the exception of showing the number of photos (estimated) that can be stored on the free space of the memory card.