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Well, yes, you could simply delete the old site and use the content on a new site. But you are not gonna get your ranking back, since the site will be a brand new one, and we know that links rank pages not content, so just because you have the same content of the old site, doesn't mean your new site is going to gain the same old ranks that your old site had.
Having said that, I read somewhere (can't recall where, but it was one of those "respected" seo blogs that one of their clients had gain their ranking back by simply deleting the page that had caused the penalty. So, if you were building most of your link to a main money page (not the index page of course), you could delete that page, and since all those links will go to 404, presumably the penalty will be lifted.
I have one site that fits that bill perfectly. I had built 50% of my heavily anchored links to that page. I have actually sent reconsideration request a few times and the site hasn't recovered yet. I am waiting for the decision on the last request, if it doesn't work, I am going to delete the page to see if it works.
Having said all of that, I would still go with a new site either way. It is incredibly easier to rank new sites with a balanced on page SEO and not much backlinks these days.
In the last 14 months or so, I have built 4 new sites, 3 of them are already making money and have ranked for most of their keyword on first page. The 4th one isn't there yet, but all the keywords are ranking, though, not on the 1st page yet.
Sure, backlinks still reign supreme, but its much easier to rank a site nowadays without backlinks (or at least with very little backlinks) than it was... say 3 years ago.
Either way, good luck with your site.