RE: MS Great Plains 2013 R2
Here's what I would do:
1. Look what modules of GP 2013 R2 are currenlty installed by using Add/Remove Programs, selecting GP 2013, and Change > Add/Remove Features. Make a note of what to install and what to leave unchecked.
2. Grab the GP 2013 R2 install media from the server it's installed on. Your former consultant should have saved it in a software share somewhere
3. Take database backups of the Dynamics and GP company databases as well as the CaptureLogins SQL script from the KB article provided already
4. Copy all of them to a new SQL Server running Windows Server 2012 R2 and SQL 2014 (you can't go newer than this)
5. Restore the databases and output of the capture logins script
6. Install the exact same service pack of GP and install the exact same GP modules you were using previously and point it at the new SQL server
If those steps don't work, then you'll need to engage a GP partner.