I don't recommend starting fresh for a few reasons.
1. In most cases, you can recover from a penalty. It is all about finding out what that penalty is. A lot of people get too caught up on what they read, or get caught up on back links when the issue might be much more simpler than that. I would suggest a site content/design redo before I would suggest starting fresh.
2. We are all set in our ways. We are likely to repeat the same mistakes that we made with the first site. Building up a new site from scratch only to suffer the same fate is debilitating. With enough persistence and effort, you can recover from just about anything if you stick with the fundamentals.
As far as how to tell if backlinks are the culprit of a ranking loss, its hard to say. It depends on the competition for that search phrase as well as on site factors that could be holding you back as well.