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My site is almost 8 years old.  So, age is unlikely to be the problem.

We are talking about internal links.  Why would Open Site explorer not see any internal links?  Could it be a bug?

Almost all search engines ignore the keyword meta tag.  In fact, you should remove that tag altogether.  So, your best bet is Google places.  Another on-page tactic is to pick a page and add the zip codes with an appropriate phrase in front of each location/zip code.