Didn't find any traces of anything firewall-related at all, using both CCleaner and Revo. However, I learnt the computer had 2 annoying infections that I couldn't be bothered to get rid of. Good old-fashioned reformat solved it all.
Many thanks for the help though, it was not in vain - I learned a few things

Also, the speed-issue has been tracked down by tracing the DNS, which leads to an old ISP we haven't used in months. The household is basically paying ISP #1 for 2.0mbit, while connected on ISP #2's 0.5 line (and this has changed after being connected to the 2.0 one for several months). Thumbs down on that one!
Again, thanks for the help!
