You could move all the files and database to the new server. You can then edit your config-inc.php file and edit the $PP_PATH and change to the new server path and change the database connection info to the new database
You should be up and running then but no photos showing so login and go to the global options and storage options and change the server path to the uploads and data directories to the new paths. You will then via ftp need to reset file and directory permissions per the install docs
http://www.photopost.com/installphp.html