I just got my starter replaced but right now it will die while running.

I strongly suggest to bring your Audi to specialty shop that will be able to diagnose the problem. Audi is very easy to diagnose if one has proper tools. There is several reasons why engine stalls while driving. Seems like you may have a problem with transmission range sensor too, as engine should start on Park and on Neutral. I'm sure you have "Check Engine" light on, there are error codes registered. I'd start there.