Move Wordpress Blog to New Host with Same Domain

My website (Wordpress blog) has outgrown its shared hosting account. We need to get on a dedicated server that can handle the volume of traffic we've been getting (25,000 - 50,000 hits per day...Alexa Rank = 45,000). Hostgator has already shut down my site on the shared reseller hosting due to excess CPU usage. It's been down for two days now so we are in a bit of a rush. We need to keep the SAME domain name, but move the entire Wordpress blog over to a dedicated server that can handle the traffic level (I'm open to suggestions). I started to do this myself but seem to have screwed it up royally. We need to export all posts, images, template, plug-ins, etc (database export?) and move everything over to the new host. I already did a "Wordpress export" of all posts and copied the wp-content directory to my hard drive. We also need to setup the new dedicated server, private nameservers, etc. Just let me know when the blog is all setup with posts populated and I'm ready to start posting again. I can provide all logins for Hostgator, my domain registrar, etc. Please let me know ASAP.