Domain expired, moved to new host, now can't access WordPress Blog

I have a web administrator who does this but I’m not uber-techy so any ideas even techie ones will go to her. My domain expired on one host and I renewed it on a new host. I still have my hosting account live and active on the old host as well as a new hosting account. WordPress doesn’t recognize my new server. Do I need to tell wordpress where my domain is now? Can I just point to the new server or do I need to backup my files off the old server (post and photos)? Thank you