After trying quite a lot of things, I have managed to have BAWstats module (sort of) working :)

What I basically did after installing and configuring the AWstats, was copying the lang, lib and icon folders, into awstats folder under sites/all/modules/bawstats. Then on the Drupal's Administer -> Site configuration -> BAWstatistic, I set all AWstats' folders to point to those folders.

The stange thing is, does not matter what I put in the AWstats icon directory:, I always get the warning message: Warning, the AWstats icon path "(AWStats folder that I set)" is not a directory. It does not work when I set the AWstats icon directory: to sites/all/modules/bawstats/awstats/icon, or any other kinds of folder name. There is no icon being displayed in Administer -> Reports -> View Site Statistics. It only works when I set it to http://my web server/sites/all/modules/bawstats/awstats/icon.

I am not sure if I shall raise a bug report for this.