Okay, how do you fix this:
There is a problem with this website’s security certificate.
It is not the site, I get no such message on my laptop.
Just guessing, but it sounds as if you have IE 7 or 8 on one system and IE 6 or 7 on the other.
Many legitimate websites let their security certificates expire due to cost.
There is a way to inspect the certificate and then accept it and install it as a trusted certificate. Let your browser guide you through the process.