Hello,
My suggestion is to give your laptop a fixed IP address in the routers subnet. i.e. if your linksys is at 192.168.1.1 use an address of 192.168.1.50 for your laptop.
IP 192.168.1.50
Subnet Mask 255.255.255.0
Gateway 192.168.1.1
DNS Server 192.168.1.1
And see if yo get internet access. Also try pinging from a command prompt on the laptop. Try the following and post the results..
ping 192.168.1.1
ping 4.2.2.2
ping google.com