Laptop Won't Recognize Internet Connection

Due to the untimely demise of my old wireless adsl router (after an altercation with a destructive toddler), I've bought a new one.Connected it via cable to my laptop, & have set it all up through the wizard. When I'm connected via cable, I can access the internet perfectly well.However, if I try to connect using wireless, it can see the wireless router, asks for password, tells me I'm connected to the router - but it tells me that I'm in a local network only (can't find the internet). I've connected another laptop and a few smartphones to wireless, and they all work without any problem at all.I've done the usual take it all apart & start again, but it still comes back to the same problem.The only thing I wondered was that the new router is Wireless N, whereas the old laptop is a b/g - but we've got an older HTC smartphone that's only b/g and that doesn't have any problems.