Occasionally, the SQL Server Service that runs the CRM Database will need to manually be started, especially following Windows Updates. The following steps walk through the process to restart the service.
To restart the service, first, take note of the Instance Name of your database, which is the part after the '\' in the Server Name window on the Login Screen:
Next, from the server PC (your PC if you're a single-user) click the Start button in Windows and type "Computer Management" without the quotes. You should see an option appear:
Next, click Services and Applications  > SQL Server Services  and then right-click on SQL Server (DATABASE NAME)  and select Start:
Once started, you should no longer receive this error message when opening your CRM.