Login to your vbulletin admin control panel. In the left menu, scroll down to the bottom untill you see "Maintenance". Click on it and a link should appear called Database Backup. Hope you can manage it from here.
Do you, or did you have shell access, and if so, is it functioning. I believe you could get your database info ussing SSH. But if your host is shut down, as in no longer in existence, the yes, you are in fact screwed as previously stated.