Unfortunately, it can be very difficult to separate a bad history from a penalty from a large-scale technical problem, especially on large sites. I've seen many people assume they got hit by Panda when it was really a link-based penalty, and vise-versa. The site's history makes this go from difficult to nearly impossible, at least without a very deep dive, but I'll see what I can see.
Alan's right on one thing - Google Webmaster Tools has huge gaps in what they warn you about, and it's typically only manual penalties. Many sites have massive problems that never trigger a warning from Google.
I notice that you're NOINDEX'ing even high-level pages (in the navigation), such as:
http://dajaz1.com/music/alternative/
That seems like a bad message to Google - if it's important enough to appear in navigation, it's important enough to index. That's a pretty extreme culling of pages.
The paginated content is a bit of a mess, such as:
http://dajaz1.com/page/350/
In some cases, these don't even seem to return any results, so I'm not sure how they got crawled in the first place. The trick with META NOINDEX here is that, until Google re-crawls, they won't process the tag. This gets tricky, but I'd recommend a couple of possibilities:
(1) If the page returns no results, 301-redirect to the last page of search that has results.
(2) If none of these pages have search value, you could block "/page" as a folder in Google Webmaster Tools. This is a bit dangerous, so I'd want to make sure none of these pages had search value.
Are you getting any page load (speed) warning? Hitting your site intially is massive - about 4MB, by my count, with a ton of JavaScript, most of which just fuels the top, rotating images (which are loading very slowly on my machine). It seems like overkill, both from an SEO and usability standpoint, and is probably in your way to recovery. I'd seriously consider stripping down the size of the code and pruning back some of the active elements for a while.
If you can re-open the important paths, get rid of the thin content (this is going to be complicated and probably involves multiple steps), and speed up the site, you'll know enough to see if this is a technical issue (such as Panda).
There is certainly weak ranking even on your indexed pages, which could indicate a penalty, but it's really tough to tell. Too much of your content is competitive or uses shared phrases or videos, so it's hard to see whether a search for:
"Dwayne Wade 70-Foot Buzzer Beater" ...has you in 6th place for competitive reasons or because your site has been devalued. I don't think it's a penalty, at least in this case. It's a YouTube video and there are other, similar videos for a fairly recent, competitive term, so this may be an accurate ranking (in Google's POV).
The history is a lot tougher, and Q&A just isn't adequate to comment on a situation that complicated, as there are not only SEO but legal ramification. Honestly, I'd have to know a lot more details on that. If you suspect the history has hit you permanently, there may come a time when you have to completely re-brand and re-launch under a new domain.
I suspect, though, that cleaning up the crawl problems, removing the thinnest content, speeding up the site, and generally fixing some technical issues could help quite a bit. It's going to be a difficult process, though. The thing about changes like the Panda Update, is that it's not just one factor. I can't point to one thing and say "fix this" - you have to aggressively attack multiple factors, since Google is wrapping multiple signals into Panda and won't tell you which one is the problem.
I should say that I'm not saying this is Panda, but that it's a Panda-like situation - you've got a lot of crawl/index issues that are going to cause you problems. The question is whether those are compounded by your history (and, unfortunately, they probably are). The combination means that you have to be even more aggressive with the clean-up.