When exporting from Timetabling Solutions desktop application you will be required to enter start dates for classes.  

These dates are not stored in Timetabling Solutions timetabling data files, they are stored in a file called LissData.xml, located in your Timetable Data folder (usually off My Documents).

If you attempt to export to Compass from a new machine, the start dates will not be present and will need to be re-entered.

However, you can copy the LissData.xml file from the original machine and paste it into the Timetable Data folder on your new machine.  When exporting to Compass it will read the dates from this file.