I Would Like to Live Off the Grid

I've always dreamed of a little cottage on a deserted Caribbean island, all by myself. I would make a roof out of solar panels for electricity, install some kind of system to desalinate the sea water to have tap water, and have either a boat or a seaplane to travel to the nearest port for food and supplies. Of course, this cottage would have the most modern of amenities inside, including satellite TV and high speed Internet, but that may be asking too much.