My blog (and server in general) is up again! I still host it on that puny server. The problem was however that my parents ISP earlier misbehaved with their DHCP-server, and their front line support not knowing anything.
ComHem has however since been bought by Tele2, and while I can't vouch for their customer service, they have at least configured their DHCP server correct, allowing both their home router and this server to get their public IP:s as expected.
Now we just hope that everything keeps working until we finally get IPv6.