Well, it sets up the html file as it should, but it doesn't output any data. I read the FAQ/Troubleshooting, and this is what I found:
PROBLEM: AWStats seems to work but I'm not getting any results. i get a statistics page that looks like i have no hits.
SOLUTION: That's the most common problem you can have and reason is simple: Your log file format setup is wrong.
If you use Apache web server
The best way of working is to use the "combined" log format (See the Setup and Use page to know the way to change your Apache server log from "common" log format into "combined").
Well. I've specified in httpd.conf that I want my logs to be combined:
CustomLog /var/log/apache/mylog_access.log combined
So, what else can be wrong? The FAQ covered no other reasons.