Well, I finally got it sorted out. It seems that my httpd.conf had been wiped out and when adding
it worked like a charm again. I don't know if it is a permanent fix, but at least it works for now.
But I also see some PHP-related warnings in the ISPC Cron log. Is that something to worry about, or can I just ignore them? It seems only to be warnings about deprecated modules which already have been loaded, and still exists in the ini-files.