Well, when I try to open my frontpage I get the "No such file or directory" error message. I've been working with Moodle for 2 or 3 years, but I haven't got a message like this yet. And it doesn't look like a Moodle error message... In Firebug I only see this source code: <html><head></head><body>No such file or directory</body></html> so I guess it is not a Moodle message.
OK, I tried to set up debug mode in config.php, but unfortunately I didn't get any information about the error...
I also created another dump from my old database and imported again but the result is the same.
I think there is something in my old database (as I mentioned: if I switch to a freshly installed database, everything works fine - but I miss all of my old data) what causes the problem.
My last idea is: import my old database table by table and check which one is the wrong table.