We are trying to transfer our wordpress.com site to a new server.
WordPress.com is a hosted blog service. You do not have to download software, pay for hosting or manage a web server. WordPress.com does not permit uploading themes or plugins. WordPress.org is free software. You can install themes and plugins, run ads, and edit the database. Check out our article on the differences.
We do not have access to the database on free hosted WordPress.com blogs. What you propose cannot be done. If your WordPress.com blog is being free hosted here then transferring content is done ONLY by export and import. The content you can move by export and import is posts, pages, comments, custom fields, categories, and tags and links. All content in text widgets must be copied and pasted. The theme cannot be exported.