Verizon to Fairpoint DSL Internet Connection

Hello,
I am a Verizon DSL customer and will be switched to FairPoint the week of February 1.

I do have one concern. As a Verizon customer, when I boot up my computer, Verizon software is engaged that establishes an automatic connection which is "up" very shortly after boot up. I receive a popup message saying "You are now connected to Verizon Online". Then I'm able to click on my IE icon and away I go.

How can I establish a connection without the Verizon software? I've tried to disable the software; tried to get it not to engage at boot up; I've tried to make a new connection - CONNECT USING A BROADBAND CONNECTION THAT IS ALWAYS ON; but have had no luck. I'm concerned that since I'm no longer a Verizon customer, my Verizon connection will be lost at some point.

I'm wondering if Verizon's software is overriding everything I'm trying to do - but I'm extremely reluctant to remove the software and then have NO access to the internet.

I've tried to contact Verizon and they refer me to Fairpoint...which puts me on hold if I ever get that far!

Anybody..please help! (I apologize for being quite so unsavvy!)
Thanks
Sandra