No VM involved (mentioned earlier but easy to miss).

Version is 2012 SP1. I will be installing CU2 this Saturday night.

It's funny you mention the physical problem, I mentioned to our infrastructure guys that it almost looked like someone was sitting at the rack popping out RAM, giggling, and then sticking it back in.

I've opened a premier support case on it, but I didn't want to 😛 I don't claim to be playing on the same field as Gail and a few other regulars here, but I have been working with SQL Server for a bit over 10 years and it's not often I get totally stumped like this.