Thanks for your help. This step-by-step process has done the database move successfully for me (moving to different machine/IP with same OS, same installation path, same DB provider):
ON THE SOURCE MACHINE:
Stop IIS
Dump theopenem database.
Save the Toems-API\Web.config DbEncryptionKey
Copy the database dump to the destination machine
Restart IIS or leave down if not going to use anymore
ON THE DESTINATION MACHINE:
Install and configure Theopenem server to make sure its working
Open the source machine database dump in text editor and replace the source machine IP address with the destination machine IP. Save.
Stop IIS
Restore theopenem database dump.
Replace the DbEncryptionKey in Toems-API\Web.config and Toec-API\Web.config with the one from the source machine (step 3)
Restart IIS
Update Toec-API\Web.config ComServerUniqueId with the one from Admin\Client Com Servers
Delete the old Toems CA and Toems Intermediate certificates if existing
Export and Install Certificates from the current database.
On the previously connected computers, deinstalling the old server' exported Toec client and reinstalling the one from the new server caused successful inventory refresh on next checkin.