Thanks for the help!
In which dump file did you see "sptd.sys"? I couldn't find it :/
Alright, I've uninstalled that file now, so I guess I should just wait a couple of weeks to see if the problem is fixed right? (Like I said, there are usually long intervals between every "accident"...).
If the computer hangs again, then I'll go on to the next step in the guide!