you need to have more try blocks, and you tried to execute the query when it should be in a try block. i would use a ResultSet interface to get the results of your statement as well...might as well use the java.sql package

plus there are a few other things that are wrong. anyway, this should clear up your troubles. also, i would suggest moving the connection attempt to a constructor somewhere. keep the java questions coming...
try{
Class.forName("sun.jdbc.odbc.JdbcOdbcDriver");
Connection databaseConnection = DriverManager.getConnection("jdbc:mysql://172.16.4.39:3306/ssntvjp", "root", "");
}
catch(ClassNotFoundException cnfex){
System.err.println("Failed to load JDBC/ODBC driver.");
cnfex.printStackTrace();
System.exit(1);
}
catch(SQLException sqlex){
System.err.println("Unable to connect!");
sqlex.printStackTrace();
}
try{
String sqlString = "SELECT * FROM Descriptor D WHERE D.SubDescriptor IS NULL";
ResultSet yourResults;
Statement stmt = databaseConnection.createStatement();
yourResults = stmt.executeQuery(sqlString);
}
catch(SQLException e){
throw(e);
}
//something should be returned here