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No. What matters is that the page for each area that you service gets Indexed. Unique content is necessary for this to happen.

You can actually leave the links in the footer since it's a good way to distribute your page juice, I would recommend just including the location though, you're creating a very high keyword density by repeating "car service" and "nj" so many times on the page.  Chatham, Clark, Cranford, etc. No keyword repetition when you do it that way. I would rewrite the duplicate content on your pages and try to make it a little bit longer. You've got zipcodes, map, links to close towns, not too bad man. The duplicate content needs to be handled though.

Been some time since I changed this and had no luck - any ideas?

Local SEO like this is tough.  In general, I like to add local information about the city when building out the content for local sites with multiple cities.  I work with a carpet cleaning company who wants to rank for each city in three counties.  We had to create roughly 20 unique content pages and one of the ways we added new, relevant content is to add local city data to the page.  We used wikipedia to search for the county and got the city data for all the cities in that county.  It gives 2010 census data and what year the city was founded.  We then found the cities homepage and set up google alerts for information regarding each particular city (make sure you set it up for once a day or your inbox will be crazy).  We then created blog posts with the city being the category and linked back to the page with the carpet cleaning targeted for that particular city.  It seems to have worked well but I'm sure there are other ways to do it too. Hope this helps!