Can't open the Exchange 2010 Management Console or shell. I've tried the usual suspects: kerbauth is correct (on the powershell virtual directory, not inhierited, not on Default Web Site, Native/Local), I'm using the Administrator account, which does have RemotepowerShellEnabled=True, WSMan in applicationhost.config pointing to the correct location, port 80 is available on the default web site and ssl is not required, my kerberos ticket does not have an excessive number of groups, the directory the powershell VD points to is correct, PowerShell app pool is running and has been recycled. Ran the EMTshooter.ps1 scripts and they just came back with some of the above. Ran WinRM quickconfig which said I needed to create a listener, which I did. Running it again came back saying it's already set up for local and remote management. I have removed the PowerShell virtual directory and recreated it.
The source of the problem was that AD Certificate Services was installed on the machine, including the web service. Apparently, installing that Role and associated Role Services changes something in IIS that Exchange just doesn't like.