first apologize for not having enough time to correct
your code,but just telling you some points.

1- you must use "setVisible(true);" in your frame
class to make it visible

2- the way you wrote event handling code is incorrect
for at least the frame  class(I am not sure with the
applet class).you must add ActionListener to your
Button.

3- For showing a html page in your applet  you should
use more complex code this is not the way,but if you
want to just redirect your page you should learn
applet to javascript integration.please consult your
references for this.