There are problems between older wireless g devices and wireless n -- both n and g routers and n and g adapters.
Symptoms I've observed range from complete failure to detect the router's signal -- to apparently connecting successfully and then losing connection at 5 seconds intervals.
However you should check the router's setup screens and make sure the router is set as a Domain Name Server.
Also check the computer's TCP/IP Properties.
Start, Connect To, Connection, Properties, Scroll Down TCP/IP and highlight, click Properties and check that Obtain DNS and IP address automatically are enabled.