I know that this is probably a late reply, but I figured that I would reply anyway in hopes that you get this and it helps, or it prompts you to post about your experience here for others.
I initially setup OST on a linux box under Apache with a local MySQL implementation. It was really a test bed box, and not intended as a final solution. So we let people test it out and they really started using it. Our production server is a Microsoft Server 2008 running IIS7 and MySQL. So I had to migrate from one server to the other. Here's what I remember of what I had to do to achieve this.
1. copy the directory (and all sub directories) of your OST installtion.
Put the copy in their new home on the new server.
2. create a back up of the database. On the Linux box I ran something similar to:
mysqldump -u username -ppassword ost_ticketdb > backup_ost_ticketdb.sql
3. Use the back up file to restore the DB on the new server. I used MySQL Administrator to import the DB from the .sql file.
4. I setup a MySQL user with an identical name and password as the one on the old server. If you cannot remember what you used that information is stored in your ./include/settings.php You can search that file for "#Mysql Login info" and it should be immediately following. It would look something like
define('DBTYPE','mysql');
define('DBHOST','localhost');
define('DBNAME','ost_ticketdb');
define('DBUSER','username');
define('DBPASS','password');
Make sure that you give your new MySQL user permissions to access the database you just created. (I don't recall the exact permissions required so you might want to check the old users permissions).
5. Lastly I setup IIS to serve the page from the new directory (step1).
Then tested by loading the page. I don't remember having to change anything else, but you may want to log in as an admin and check the upload dir path if you allow attachments, and help desk url if you changed the hostname/domain name.