I've had the same trouble with Verizon, I'm still waiting for them to send me my new password, it's been over 10 days. When I go to the website it says:
If your device cannot receive text messages, please proceed through the Forgot Password screens and your temporary password will be mailed to your billing address. Once received, sign in to My Verizon using your mobile number and temporary password.
But this puts me in an endless loop of asking for my cell phone number. I have tried a multitude of different ways to type the cell number verizon gave me but it still just loops back. I posted about it on Verizon's facebook page but I doubt that will do any good. They don't seem to care about giving good customer service.
Has anyone found out how to get them to send you a new password?
Thanks