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Chris. ->> Links are advertising NOT optimising!! <<-
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AdSense is what rejected you not AdWords. Without knowing more about your site there's not much advice anyone can offer though. You saying the site is clean doesn't make it clean. It also doesn't mean if meets any standard Google uses to allow you to use AdSense.
It's up to them whether or not to let you in, but usually you have to be doing something they don't like if they won't approve you.