We moved hosting for a website that we were using the WonderPlugin Carousel. The carousel information was lost in the transfer.
I still have access to the old server files. Is there a place where I can go and find the old carousel files and copy them over to the new host? Or am I screwed and have to rebuild all of them?
The carousel information are saved in the WordPress database, the table name is wp_wonderplugin_carousel.
If you move your database together with your website files, then it's supposed to work fine.
Actually, WordPress is database driven. Most of your website content are saved in the WordPress database, for example, the posts and pages content. So if you move the hosting, you need to move the database together with the files.
You can view the official document about how to move WordPress: http://codex.wordpress.org/Moving_WordPress