I'm sorry, but deleted blogs cannot be restored or reused. Deleting a blog is permanent and the name cannot be used again. There are several warnings about this on the Tools -> Delete Site page and in the help pages, and you are required to confirm the deletion by email.
http://en.support.wordpress.com/delete-site/
You can start a new blog by logging in to WordPress.com and then going to http://en.wordpress.com/signup/
With any blog, you can also use your custom domain with Domain Mapping upgrade. http://en.support.wordpress.com/domains/