I am a web developer and upgraded 14 WP sites last weekend. I highly recommend that you upgrade incrementally due to close-to-the-bone changes in the database structure along the way.
There was no WP 2.4, so your upgrade path should be first to 2.5, then to 2.6, 2.7, and finally 2.8.4. It may seem like a pain in the butt, but really, you’re better off.
Before you start, don’t forget to DISABLE ALL WP PLUGINS. Don’t reactivate them until you’re done upgrading. And also don’t forget that you should overwrite all the *.php files in the root, and everything in the /wp-admin and /wp-includes folders.
DO NOT DELETE OR OVERWRITE .htaccess, wp-config.php or any robots.txt files you have.
After each upload, navigate to the /wp-admin/upgrade.php file, click through, and perform the upgrade.
After you’ve upgraded to 2.8.4, login and make sure everything works fine. Sometimes you’ll have a plugin that stinks up the pond. When that happens, just delete that plugin from the server via your FTP program if you cannot do so via the WP Dashboard. That likely means that the plugin won’t work with 2.8.4 and you’ll have to find a substitute.
I can tell you from experience that the main plugin I’ve had problems with was the Google SiteMap plugin.
Good luck!