The enterprise database specified '<Database_Name_Here'> exists, however it is not structurally valid.
Please select a different enterprise database.
If you try to create the database first and then upsize to it you will see the above message. Delete the database and its associated files. Do the upsize again. gINT will create the database during the upsize process.
If your enterprise database has become damaged you could see the above message. Restore it from a backup.