Moving SQl Server SBS 2003 to SQL Server 2014

We have a client who has refused until now to update his server and software.  The vertical application is no longer supported by the vendor and is a custom application.  So the option we have is to move the sql databases which are currently hosted on a SBS 2003 server.  We are installing a test server 2012 running SQL 2014 and will try to run the client app in a VM.
What is the easiest and best way to export the sql data from the old sql to the new.  All of the sql backup apps that run on sbs 2003 will not run on Server 2012, that we have tried.

I'm not a sql expert so need some walking through it.