First, let me say that the term “Google slap” has traditionally applied to have the Quality Scores lowered on your AdWords campaigns. Since this forum is about PPC and SEO your use of that term to describe your particular issue may mislead or confuse some folks. What you are experiencing is competition, not a slap, and probably not a duplicate content issue either.
If by duplicate content you mean you have a canonical issue, meaning different URLs pointing to the same document, there are plenty of ways to resolve this issue. This link should help you out with information on how to resolve the issue:
Google ranks webpages based on relevance, not how many backlinks you have. Backlinks can play a role in influencing relevancy scores, so if you gain optimized backlinks then, yes, they will help to influence your ranking.
As far as duplicate content goes, it doesn’t sound like that is your true issue. If your page is ranking at all then it is not penalized. Here is what Google has said about the subject of “Duplicate Content Penalties”: