I think you need to diagnose the why before you start doing things like 301-redirecting. This could be just a matter of keyword competition or it could signal a serious problem with your home-page. For a privacy page to outrank your home page isn't a good sign, on the surface.
So, first things first - the home-page seems to be indexed. That's a good thing.
As @Cardigan said, you are using the phrase "Mardi Gras Parade Tickets" in every TITLE tag. I don't think that's the full problem, but it can certainly send mixed signals. Even though that's your brand, I wouldn't trail every TITLE with it - it just makes your tags too long and removes a lot of there uniqueness, IMO.
If I search the exact phrase "Mardi Gras Parade Tickets" in Google, you've got 4 pages ranking in the Top 10, none of which are your home page. That's definitely odd. It suggests that your site as a while is doing fine, but that your home-page may be selectively filtered or penalized for that phrase. This could be the repetition, but the impact isn't usually so extreme. It could be a long profile or anchor text issue.
You also don't rank for the exact title phrase "Mardi Gras Parade Tickets 2013", which is starting to look more like a penalty situation or severe technical problem (like malware, as @Deb mentioned). You can check for malware in Google Webmaster Tools, and I'd also check to see if Google can fetch the page properly.
You don't have a ton of links, so I'm not spotting any particularly bad ones. I also don't see you abusing exact-match anchor text much. Unless you've aggressively built links recently that aren't showing up in our system, my gut reaction is that Google thinks there's something wrong with the home-page.
Sorry, I see a and probably the problem. Your domain is almost an exact duplicate of:
http://www.neworleansparadetickets.com/
...including the copy. I think Google is aggressively filtering out your domain. If you're trying to target the same content with different EMDs, you're going to need to make it more unique. Otherwise, the tactic is going to backfire on you.