Hi Will Stephens,
Welcome to Microsoft Q&A forum.
As I understand, you are getting SQL Server does not exist or access denied error.
Could you please refer to the solutions discussed over these links which might help:
https://stackoverflow.com/questions/4657919/sql-server-does-not-exist-or-access-denied
https://support.microsoft.com/en-us/topic/eb667d0e-9489-89c4-78d6-5e314bd1d806
Let us know if above do not help.
Thanks