Login failed. The login is from an untrusted domain and cannot be used with Windows authentication.

I encountered this problem today on a server running SCVMM 2012. I found a lot of things online suggesting a lot of different possible solutions, but none of them worked for me. Most of the possible solutions involved configuration errors with authentication, but this has worked fine for some time, and only today started giving this problem. Besides that, this server hosts the databases for a number of other apps, and none of those stopped working today, so after a quick check over the SQL Server settings I was left scratching my head.