Your Xpert-Timer database is stored locally as an Access database or SQLite database. If you are running the multi user version of Xpert-Timer you might use a Microsoft SQL-Database or a MySQL database. Open your System info of Xpert-Timer (in the project manager point to "Help" -> "Info..." -> System info, to find out the exact location and version of your database.
The configuration file holds all your connection data to the database. Using an MS-SQL database, then the login name and password is saved in the xperttimer.ini file.
If you are using a MS-SQL or MySQL database, you could install Xpert-Timer on your new computer and use XTAdmin to connect to the existing database on your server. This is the easiest way to move from one to another computer.