I've gone to the link that is referenced every time someone asks what the student loan limits are, but I still have this question.

The link shows a total limit of i.e.5500 (3500 subsidized; 2000 unsubsidized)

If you do not qualify for a subsidized loan is the unsubsidized limit 2000 or 5500?

$5,500, up to $3,500 of which can be subsidized. So to answer your question, if you don't qualify for a subsidized Stafford loan.. you can take out the full amount offered in an unsubsidized loan(s).