What gossipgirl said is absolutely correct. You can continue to try to shake more water out or use compressed air (low pressure) to blow water out. If possible, remove as many of the (camera) body panels as possible to help accommodate the removal and evaporation of residual water. Put the camera on top of a water heater if it's well shielded, or on a heater register. If you're in a summer environment, the camera camera can be placed on a heating pad at low temperature (150F or less).
In fresh water, and with luck, the water will blow/dry/evaporate out without damaging your camera. The fact that your memory card and battery function is encouraging.
HOWEVER, if the camera continues not to function after several days of "drying cycle" you'll either have to replace it or take in to a repair facility.