It's not a separate program- it's a separate window. If they are in the same package, you can simply instantiate the new JFrame and make sure its visibility is set to true. Otherwise, you will first have to import the other class. To get rid of the current JFrame as well, you can set its visibility to false and invoke the dispose() method on it to free up resources.

if(e.getSource() == loginButton && userNameAndPasswordAreValid){
     NewJframeClass frame = new NewJframeClass();
     frame.setVisible(true);
}

Have a look at this simple tutorial which will help you.

You're missing the Timer event (timer1_Timer()).

Look at the link above and it should tell you all you need to know.