If you have not done so already, get the internet working using a WIRE to connect the laptop to the router.
That way you prove the whole connection is working.
If it is working, and you want to move to wireless, then go into the web interface for your router and set it up. Should be explained in the router documentation.
As a start turn off ALL wi fi security on the router and laptop and close down your firewall.
Once it is working then you can turn on the wi fi security and turn on your firewall.
Your router documentation should give simple step by step instructions on how to set up wi fi.