As a side note, there shouldn't be a great deal of issue using Google Analytics internally (if I understand your scenario correctly). If the users when visiting your internal-only webpage have access to the internet, the Google Analytics code should still fire and log a stat. (As the code is running on the client - its only them than need access to the internet). We use this setup where I work to monitor user stats for our Intranet just fine.
With regards to AWStats. I've had quite a large amount of success with it parsing the Apache log files. The extra info in GA is quite useful though at times to grasp your demographic and average settings for user pc's.