Are you playing on the same Xbox that you bought the songs on? If not then you need to find a way to hook your Xbox to the internet so you can do a
license transfer. Every piece of DLC comes with 2 licenses, one is tied to the Gamertag that it was bought on and the other is tied to the Xbox it was bought on. So DLC on a different Xbox will only work if the GT that bought is connected to Live.
I have this problem but I've discovered that when I did my Licence Transfer from my old 360 to my new one about 15 of my DLC stopped working. After checking my purchase history none of those songs were in my history thus they can no longer be played. How
do I fix this? I clearly downloaded them but xbox.com reckons I never did. Harmonix and their forum is totally useless.