Before redirecting everything, consider if it's your content that has the problem or if it's the backlinks that were devalued.
Around the time you saw the drop, many "low quality link" networks were under fire. As the link networks were devalued, so were the sites that they were propping up on the SERPs. If your problem is related to penguin and bad links, redirecting to a new domain would do little to solve the problem.
To cap your questions, it's unlikely that you are directly penalized. Google's algorithm probably decided that your site isn't offering anything that warrants high position in the SERPs (right or wrong) so your traffic fell off to match.
One step you can take is to figure out if all of your pages lost incoming traffic or if you just had a few pages that were keeping your traffic so high. If it was only a few pages drawing all the traffic from google, then you may have just been lucky to grab the traffic in the first place. If your homepage lost significant traffic then it's a different story (meaning your entire site was likely devalued on its key search phrases).
For example I was working on a site that lost 20% of its traffic when google removed one page from the top position in the SERPs on a broad keyword search term. We never knew why google liked that one page because it was a terrible page. There's not much we can do to recover that page because things have majorly changed in the SERPs on that search phrase. The homepage however continued to receive the same traffic.
Force google to rank your site higher by making it a great site that offers a lot to users searching for your key search terms. Keep in mind that the landscape of the key search terms leading to your site may have changed dramatically over the years since the "penalty".