Well, if you want to start over, you can re-FTP your wp-config.php file and then navigate to wp-admin/install.php and it will reinstall itself. If you have your design in a subdirectory of /wp-content/themes/, WP will not disturb those files. It will only add the two that ship with it, Default (Kubrick) and Classic (ugh). Then you can keep working on your design and site structure (installing plugins, setting up pages, categories, the sidebar, links, etc.).
I know how you feel about wanting to keep working to get the site set up and it seems like these kind of things happen when we are right in the middle of a major milestone.
And once you do get back up on your feet, go ahead and install Skippy's database backup plugin. You can have it mailed to yourself. This plugin is tailor made for someone in your shoes, who doesn't have access to their database files. This way, you can periodically create backups and store them on your hard drive for these such occasions.
Download Skippy's plugin here:
Good luck. I'm off to sleep!