Go to the bottom right-hand corner of the screen and to the 'Connections' icon. See if it says something like:
"Connected to xxxx. Internet access"
or
"Connected to xxxx. No internet access"
or
"Not connected: Connections available"
If you see "Not connected: Connections available" and your router is shown, click to connect on it, ensuring that 'connect automatically' has a tick next to it.
If you see "Not connected: Connections available" and your router is
not shown, try turning off the router and disconnecting it from the phone line. Then reconnect it and turn it on again. Then check to see if a connection has become available again.
If you see "Connected to xxxx" (irrespective of whether 'Internet access' is shown) try resetting the laptop's TCP/IP stack. (it's easier than it sounds!):
http://www.windows-secrets.co.uk/2013/08/repair-the-windows-87vista-tcpip-stack/
If you need to post again, please tell use which message you see when you go to the 'Connections' icon and which version of Windows the laptop is running.