I suggest making sure it is not a software issue by using a different browser or ping the websites you do not seem to be able to access. A firewall or security software may also interfere with the connection, try disable it for a moment for testing purposes.
You may verify if you need to use specific DNS settings in this system which may be in use by the other systems.
It is also recommended to consider if a firmware upgrade for your router has a chance to solve your issue due to compatibility.
Check the security encryption settings in both the computer wireless profile and the router. Additional security settings on the router may limit the connection or block internet access to specific sites.
This is the latest generic driver: https://downloadcenter.intel.com/Detail_Desc.aspx?DwnldID=24521