The modem/router that you refer two has 2 interfaces, an external, and an internal. The external IP is the one that should be static and the information provided by Verizon. The internal interface should hold an address that is in the private ip address range, such as, 192.168.0.1. If you static the information that VZ gave you onto the external interface, then set the internal interface to be a DHCP server it should automatically assign your pc with an internal address also if your computer is set to "Obtain Address Automatically". You then would want to enter the configuration to the router, and on the tab that states something like Port Forwarding, Applications and Gaming, or something of the sort, you should see a screen that you can enter in a to and from port range, protocol, ip, and enable. On one of the lines on that screen, you will need to enter the port range in to equal port 80, so it would be From 80 to 80, protocol TCP (both should work also), IP address of your PC, (should now be a 192.168.0.? address), and enable the check box, save your changes, you should then be able to access the web page on your server by typing: http://<your external IP address>
You DO NOT want to give your PC and address that matches or is even somewhat like the address that VZ gave you. That is for your modem/router. That is why you were getting conflicts when both were plugged in together with same IP. You cannot have matching IP addresses on the same network.