Business group going to DC
Elyssa has some good suggestions if you want all 35 to be able to eat together. In that vien I'd also look at the Caucus Room, the Oval Room, and Corduroy.
However, if you are thinking of giving the group choices that they will go to on their own, it opens up a whole range of places. Washington's strength is ethnic food, you name it we have it. (Probably only NYC has as wide a variety of choices as DC when it comes to the range of cusines to chose from.) Ethiopian is ubiquitous, there are literally a dozen good places to get it.
That's a really large group. The best idea is to find a place where you can rent out a room. I'm wondering what your price range is. But without knowing that a few places where I know there are private rooms or room for this amount of people:
*Prime Rib--not sure if there is a private room but its certainly a delicious, old school DC place