Recently my hard drive crashed and at the same time my WordPress blog stopped working. After looking into it I lost my database file and I don't have a backup (stupid) I'm new to blogging and had no idea about databases.... I'm assuming that the database must have been on my local computer and not the server for some reason. I'm guessing there is no way to recreate the database without starting over? If this is the case, how can I get my site up and going again? Can I just add a new database or do I have to start over?
I would be very surprised if your database was not on the server unless you are running WP locally. Can you log in to your hosting account?
Who is your host? Maybe they have a backup of the database.
Typically, the database is maintained by your host on the host database servers.
If you can't secure a backup of the database to restore then you'd need to reinstall WordPress (start from the beginning). If you do reinstall, download the latest copy of WordPress 2.3 and follow Installing WordPress.
Also please read WordPress Backups.