How do I get my downloaded xbox live games on my new system?

I sold my xbox 360 over a year ago. I am thinking of purchasing a new xbox arcade system along with a used hard drive. Will I be able to download the games on the new system? I do not have access to the old hard drive because I sold that with my old xbox 360. I kept my xbox live account (and can still log into it online). How do I get my downloaded xbox live games on my new system?
Yes, you will be able to get your games back, all you have to do is log into your Xbox Live account and go to the game you want back and select 'Re-Download' this should get you your old games back.