|Yes the basic concept is wrong. You need a router if you want to share the Internet connection. The modem pugs into the router and the wireless access point plugs into the router.|
The router will have Network Address Translation which allows to computer to share the same public IP address via two or more private IP addresses. Aa you have it at the moment you are trying to share a the same public IP address between two computer and it wont work.
You should really have got a wireless router which is a router, wireless access point and switch all built into the same box.