Aaaah, I finally found it.
The proxy settings in Internet Options -> Connections -> LAN Settings was enabled!
I turned it off, and voila! it worked again!
Puh, that was a hard one. Two things made that hard to find:
1. I never dreamt that WebEPG.exe used the proxy settings from there.
2. I don't use Internet Explorer, I use Firefox, and in there the pages worked fine.
Don't really understund why it doesn't work with through a proxy, though.