Thanks, Alexander and Matt! I didn't expect to get any replies so soon!

I don't necessarily need to transfer the domain name if something simpler would do, but I seem to be stuck - I can get into my control panel, but I don't see anything about nameservers or DNS when I'm there, just a lot of icons. I think Alexander is right, I'm just going to have to wait until someone at my old host gets back to me, but I really appreciate your responses!