I recently got a Verizon USB720 for my MacBook Pro and installed the software that Verizon provides. I frequently use the Cisco VPN software to connect to my clients’ networks to do work and I also use Parallels to test software on Windows.
There’s a little known (as far as I can tell) interaction between the three, where the Cisco VPN won’t allow you to connect anywhere and if it does, only for a few seconds. To get this feature back, all you have to do is disable the network ports that Parallels creates for NAT networking when you’re connecting to the Verizon card.
Go to System Preferences > Network > Network Port Configurations and uncheck the boxes that say Parallels like the image below.
Once you do that, you’ll be able to connect to the VPN just fine.