Try booting in to safe mode with networking, (reboot tapping F8 key ) try IE again.if this works then the most likley reason is you have a virus while in safe mode download and run malware bytes and superantispy
Have you run malware bytes and superanti spy download them to a stick or another machine and copy to machine you are having problems with run them both 1 at a time delete anything they find then try again
the machine you are replying on now is obviously working is this machine conected to router by cable if so remove cable from working machine and conect to laptop and try this if that dosent work try rebooting laptop with cable conected
Once you have done that conect back to working machine and let me know what happens
First of all...are you using a wired connection or a wireless connection to connect to the internet??
Check your ip address, subnet mask and gateway ip. First try to ping your gateway ip address, if you are able to ping then try to ping the ip address 126.96.36.199 or any other public ip address. If you are able to get reply then the issue is with the browser settings or the DNS address.
If you are connecting wireless then delete the wireless profiles search for the networks and then try to connect.
also try turning off the wireless on laptop leave for about 10 secs and turn it back on again if no joy turn off router leave 10 secs and then turn on again if still no joy then try running a restore what os system are you running