There are lots of reasons for this...
Sometime it is seen that older versions of laptop fails to give internet access when there is any new advance laptop is already connected. It can also happen due to mistakes in some configurations. There are some points to check....
Click on Start, then Run and type in 'services.msc'. Down at the bottom is Windows Zero Configuration. If not started, right click on it, Properties. Startup Type should be set to Automatic and then click Start and then Apply.
Check for firewall settings.
Go to browser settings and uncheck the "use proxy server", if it is checked. There should be no proxy servers.
Go to command prompt and type 'ping google.co.in'. See if it gives any IP address. copy that IP address to browser's address bar and hit enter.
Go to control panel>network connections, see wifi connection icon. Right click and go to properties. Check for any flaws..