I'm still not following you. Maybe I'm just not up-to-date with the terminology or something.
What is an "internet key" exactly? Some sort of USB modem? DSL? Cable? 3G?
You can change DNS settings in the "Network" pane of the System Preferences. Are you saying that when you input the proper DNS settings that you can no longer connect?
What is "without the program?" What "program" are you talking about? With whom is the service through (Verizon, Orange, etc.)?