The big thing to remember is that Java is a case sensitive language.
There is no "Service" method (with an upper case S). So you haven't overridden any of the required methods needed to support a GET request.
Also, overriding the service method is not a good idea (except in rare cases). It is better to explicitly override doGet and doPost. If you want the same code to handle both methods, have one call the other or have them both call a user defined method of your own.