I tried to install Exchange 2013 with the resource windowsProcess in existing Exchange Configuration. All prerequisites are installed (the Exchange Organization still exists).

This is my Resource section:

       WindowsProcess Exchange2013  {
            Credential=$credential
            Path= "C:\Sources\Cumulative Update 5 for Exchange Server 2013 (KB2936880)\Setup.exe"
            Arguments= "/mode:Install /role:Mailbox /IAcceptExchangeServerLicenseTerms /TargetDir:C:\EX2013"
            Ensure= "Present"               
       } #End Filter

  } #End Node

} # End configuration

/*
  @TargetNode='TargetDSC02'
  @GeneratedBy=exadmin
  @GenerationDate=08/02/2014 08:16:03
  @GenerationHost=SOURCEDSC02
*/

instance of MSFT_Credential as $MSFT_Credential1ref
{
    Password = "Password1";
    UserName = "S05\\Exadmin";
};

Exadmin is a member of Orgaganization Management Group and it is also member of Domain Admin Group, to be able to install Exchange

When I execute this resource , Exchange Installation Start but after 1 minute the installation stops with this error:

Failed [Rule:GlobalServerInstall] [Message:You must be a member of the 'Organization Management' role group or a member of the 'Enterprise Admins' group to continue.]

To be sure that the right is really the problem

I create a special User with only Administrator right of the Exchange server and with no Exchange Permission

I run manually on the new Exchange server .\Setup.exe /mode:Install /role:Mailbox /IAcceptExchangeServerLicenseTerms /Targetdir:C:\EX2013

And I got the Same error that with DSC.

After I add my test user in the Organization Management Group and I run again manually .\Setup.exe /mode:Install /role:Mailbox /IAcceptExchangeServerLicenseTerms /Targetdir:C:\EX2013

And the Exchange 2013 installation finish without any error.

That prove that the problem with DSC is Permission right.