at first check "internet options" in Internet Explorer (or via Control Panel). Perhaps some parental control options are enabled.
Additionally, have a look at the hosts file (usually in C:\WINDOWS\system32\drivers\etc).
Also, this problem could be due to some 3rd party "firewall" application.
But since you want to give that laptop away, I'd rather suggest to reinstall the operating system on a fresh formatted HDD. (and don't forget to install all updates)