I think I got it now:
I changed the following:
base_url = "http://www.scienca-revuo.info"
base_url = "http://scienca-revuo.info"
base_url[sr] = "http://www.scienca-revuo.info"
base_url[sr] = "http://scienca-revuo.info"
This did the trick for some reason, but only in combination with the patch http://pkp.sfu.ca/bugzilla/show_bug.cgi?id=7957
Still I don't understand why as I have a testing site using the base_url http://testo.scienca-revuo.info
with the same configuration, which works. Why would it work with "testo." but not with "www."?
Anyhow. I can live with not having www. in front, so the problem seems to be solved for now. I tested it now with two versions of IE on three machines. More tests I will do, when I have access to differen windows machines.
Thanks for your help and patience. Hopefully I will not need to come back with this.