This is kind of a stretch as far as my knowledge about installing apps like this, but since nobody else seems to know what the problem is either I'll try to help out.
Your directory structure is kinda weird; that threw me off a bit. Is it just that your username and the domain name are the same?
What's the path to your log file in your awstats.domain.com.conf file? (Mine is LogFile="/home/username/logs/domain.com/http/access.log.0" )
My install does look a lot different from yours. My awstats directory is outside of my webspace, at /home/username/awstats/ I don't know that installing it where you did should cause any sort of problem, but if it's still not working after all this time, I wonder if it might be worth a try to remove it altogether and reinstall using either these instructions: http://wiki.dreamhost.com/index.php/AWStats_Installation or these ones: http://wiki.dreamhost.com/index.php/AWStats_Installation_(alternative)
Even if one of those is what you used before, maybe something went wrong during the installation. The first set of instructions is what I used & it got me up and running fairly easily.
Or, an alternative, this post has a link to an awstats package that a user here set up for updating via the browser -- I haven't tried this yet, but maybe it'll help you out.