First install PostgreSQL on a new server.

Close the DISE Server services and export the database to an SQL file (you could move the pgData folder as well, but that may not work if you are moving to other OS or PostgreSQL version).

Use a command like this to export into SQL 

"C:\Program Files (x86)\DISE\DISE Server\pgsql\bin\pg_dump.exe" -U dise -b -C dise > backup.sql

And a command like this to import 

"C:\Program Files (x86)\DISE\DISE Server\pgsql\bin\psql.exe" --username=diseserver -d dise -f backup.sql

Then you need to disable the DISEServerPGSQL service on the original server

and using regedit, change the following key, and remove DISEServerPGSQL

HKEY_LOCAL_MACHINE\SYSTEM\ControlSet001\Services\DISEServer\DependOnService

Edit and run the attached reg file to change the database settings of the server. 

And then last run the DISEServerInstaller.bat file from the DISE Server installation directory. This will update the database settings to use the new server.

Now the services should be up and running and using the new database server.