If its anything like DA:Awakening disc, you would put that disc in to play awakening and the original disc to play the original story.
When you select 'new game' it gives you options of which story you want to start based on the modules currently available.
EG, with original disc in I get DA:O or Liliths song (Becouse I downloaded it), with DA:A disc I get DA:A or Liliths song.
I guess, if I downloaded everything but the original DA:O I would have them all as an option on 'new game'
Anyway, try just running the second disc, it may tell you what you need to do if it isn't the above.