I encountered the same error (...Perl56.dll...) when I was using DBI and didn't have the right version of the module installed. I tried reinstalling perl to no avail. When i installed the right version of DBI it went away.

Now i know nothing about AWStats... but does it require some module that you may have the wrong version of for your copy of perl. If you're on winxp im assuming you're using activestate... pull up the package manager and look to see if there are any modules that could be updated... that's all i can suggest