When I first start up the game and access the main menu, if gives me a pop us stating something about "Downloaded content not accessible". But when I go to the dashboard and memory section, it clearly shows the Anarchy edition, Sewer levels and 8mb Update. My internet has been down the past 2 days and didn't know if this plays an effect on me accessing downloaded features.

This sounds similar to issues reported with Fallout/Oblivion DLC when they take their game offline. Content is not only tied to your gamertag and HDD, but also the console it's downloaded on. If you're now playing the content on a different Xbox, you would need to do a http://www.xbox.com/en-US/Support/LicenseMigration/Home.

Ah, that's my problem. I connected my HDD to another console with internet access and downloaded the DLC. I wasn't aware that the DLC was also tied into the console or I would have just waited for my internet to get kicked back on. Thanks for the help.

Can I re-download the DLC Anarchy and Sewer missions when my internet gets turned back on so i don't have to do a license transfer?

No. It'll still be registered to the old Xbox and be unavailable offline. I had the same issue with my Mass Effect 2 DLC. Re-downloaded it on my new Xbox, but when offline it was inaccessible until I did the license transfer