Hi @John Laidlaw ,
So you are trying to use the Microsoft Data Migration Assistant tool to migrate from the on-premises SQL Server to the Azure SQL database, but you cannot connect to the source on-premises SQL Server instance.
It seems that the computer hosting the DMA tool is different from the server hosting the local SQL Server instance by your description. This seems to be a remote connection issue. For this, you can check the doc: Troubleshoot connecting to the SQL Server Database Engine.