After some discussion, I find that their local network had suddenly decided to block access from the company network to the company's own css file. Not the whole website, just the css file. (Css files are text files where websites keep all their formatting information. Everyone's got one, or even several. Here's one of the ones that the current default theme on Bunn.livejournal.com uses, for example :http://l-stat.livejournal.com/voxhtml/hills/screen.css)
I can't work out why any network would block access to an inoffensive textfile that belongs to their own organisation!
They aren't allowed to contact their network administrators when stuff like this happens, so they have no way to fix it. Nobody knows why it happens. Possibly it's some kind of curse.