This is a tricky error to fix when you are trying to install SharePoint 2013 on a non-domain environment. I have run into this the most when helping clients setting up isolated development areas to for indivudal users to program in.
The exact error is:
Failed to connect to the configuration database.
An exception of type System.Management.Automation.CmdletInvocationException was thrown. Additional exception information: ErrorCode<NonDomainNWService>:SubStatus<ES0001>:Service running under Network Service account in workgroup environment is not supported.
While this may look like an error of doom for setting up a Sharepoint 2013 in workgroup, you will find it a really easy error to fix! All you have to do is to start PSconfig as so:
psconfig.exe -cmd Configdb create SkipRegisterAsDistributedCacheHost
And the error will go away!