Quote: "This is why they're never allowed to touch my computers."
I agree but I had no other way of convincing them that their network was the problem.
Quote: "Did they change network settings? Or browser settings in IE?"
I'm fairly sure they messed about with both. I suspect the problem is a network setting but can't now find one that looks familiar (since I couldn't connect I made the changes myself during the phone call following their suggestions so I might recognize the offending page).
Quote: "If you go into your network properties, check the settings in the tcp/ip and see if they match up to what your laptop says."
That sounds like the properties that I can't locate. Where are they? The problem machine is using Vista Home Premium, the laptops are XP and Windows 7.
Quote: "I'd be easier if I could play around on your machine for a few minutes. I'm trying to thing of something cache related."
Indeed.

I could be wrong about "cache" being involved though. I think things might be clearer when I locate the correct set of properties.