Chances are your probably right re. it being an ip addressing problem. Whats the make/model of the router?
In both pc and laptop, at the command prompt, type in ipconfig/all . This will show the ip address for each. If they both have the same ip, then theres a conflict either caused by having just one ip address in the routers ip address range (if dynamic setup) or just one ip address setup for both pc/laptop (if static setup).
Go to the router configuration settings (probably at http://192.168.1.1 ) and check whether set to dhcp or static.