Thank you MrWizard!
I downloaded the Motorola 64 bit driver from the Web site which he provided and then followed his instructions and manually set up a connection to Verizon from my Windows 7 computer. It works!
Following his instructions I copied the information from the old XP computer. The main things needed was the user name and the dial up number.
Since this process was not too difficult I do not understand why Verizon doesn't set it up for us. I got used to having VZaccess tell me what my usage was. Now I don't have that information. This may not matter as when we are traveling I am not a heavy user but I still felt it was comforting to know.
At least I can get online with my new computer now and can carry it with me while traveling.