General

I'll make it even easier:

www.gamefaqs.com/xbox360/959557-fallout-new-vegas/faqs


Also:
www.gamefaqs.com/xbox360/959557-fallout-new-vegas/faqs

Shows that it's a bug that you're unable to leave the room, and offers a few solutions. If you haven't killed Orion, pickpocket him for the key.