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Otherwise, you can probably find an ASP script that would work for you (you need to run it from every page tho') - try something like scripts.com or google it.
Personally, I hate those little counters. And they aren't that accurate (doubt they give proper referrers for example).
Tell your hoster to turn on referral tracking:
Website Properties-->Web Site Tab-->
Check enable logging
Click Properties -->Extended Properties Tab
Check Referrer
Click OK
Click OK
If they're not willing to do so I can only imagine it's a storage issue.
If changing hosts is out of the question, you could easily roll your own solution. Research the ASP Server Variables; there you'll find almost everything you need (IP, Page, Referring URL, etc...) to capture and stuff into your own stats table. Then you just need to write your own queries.