Cannot install Desktop Experience on Windows Server 2008 R2

I'm trying to deploy Exchange Server 2013 on Windows Server 2008 R2 in my test environment.
One of the pre-requisites is to have Desktop Experience installed.
When I try to install it via PowerShell, I get this failure message:

add-windowsfeature : Installation of [Ink and Handwriting Services] Ink Support failed. Attempt to install Ink Support
failed with error code 0x8007010B.  The directory name is invalid
At line:1 char:1
+ add-windowsfeature desktop-experience -logpath c:\log.log
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : OperationStopped: (:) [Add-WindowsFeature], Exception
    + FullyQualifiedErrorId : FeatureMessageDetail,Microsoft.Windows.ServerManager.Commands.AddWindowsFeatureCommand
add-windowsfeature : Installation of [Desktop Experience] Desktop Experience failed. Attempt to install Desktop
Experience failed with error code 0x8007010B.  The directory name is invalid
At line:1 char:1
+ add-windowsfeature desktop-experience -logpath c:\log.log
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : OperationStopped: (:) [Add-WindowsFeature], Exception
    + FullyQualifiedErrorId : FeatureMessageDetail,Microsoft.Windows.ServerManager.Commands.AddWindowsFeatureCommand

Success Restart Needed Exit Code Feature Result
------- -------------- --------- --------------
False   No             Failed    {Ink Support, Desktop Experience}

The installation log shows this:

4076: 2013-01-04 14:46:47.306 [Sync]                      Calling sync provider of Ink Support ...
4076: 2013-01-04 14:46:47.309 [Provider]                  Sync:: guest: 'Ink Support', guest deleted?: False
4076: 2013-01-04 14:46:47.312 [Provider]                  Begin installation of 'Ink Support'...
4076: 2013-01-04 14:46:47.314 [Provider]                  Install: Guest: 'Ink Support', updateElement: 'InkSupport'
4076: 2013-01-04 14:46:47.317 [Provider]                  Installation queued for 'Ink Support'.
4076: 2013-01-04 14:46:47.320 [Sync]                      Calling sync provider of Desktop Experience ...
4076: 2013-01-04 14:46:47.323 [Provider]                  Sync:: guest: 'Desktop Experience', guest deleted?: False
4076: 2013-01-04 14:46:47.324 [Provider]                  Begin installation of 'Desktop Experience'...
4076: 2013-01-04 14:46:47.326 [Provider]                  Install: Guest: 'Desktop Experience', updateElement: 'DesktopExperience'
4076: 2013-01-04 14:46:47.329 [Provider]                  Installation queued for 'Desktop Experience'.
4076: 2013-01-04 14:46:47.332 [CBS]                       installing 'InkSupport DesktopExperience ' ...
4076: 2013-01-04 14:46:56.576 [CBS]                       ...parents that will be auto-installed: '<none>'
4076: 2013-01-04 14:46:56.580 [CBS]                       ...default children to turn-off: '<none>'
4076: 2013-01-04 14:46:56.699 [CBS]                       ...current state of 'InkSupport': p: Staged, a: Staged, s: UninstallRequested
4076: 2013-01-04 14:46:56.703 [CBS]                       ...setting state of 'InkSupport' to 'InstallRequested'
4076: 2013-01-04 14:46:56.798 [CBS]                       ...current state of 'DesktopExperience': p: Staged, a: Staged, s: UninstallRequested
4076: 2013-01-04 14:46:56.802 [CBS]                       ...setting state of 'DesktopExperience' to 'InstallRequested'
4076: 2013-01-04 14:46:56.900 [CBS]                       ...'InkSupport' : applicability: Applicable
4076: 2013-01-04 14:46:57.083 [CBS]                       ...'DesktopExperience' : applicability: Applicable
4076: 2013-01-04 14:46:58.673 [CbsUIHandler]              Initiate:
4076: 2013-01-04 14:47:32.928 [CbsUIHandler]              Error: -2147024629 :
4076: 2013-01-04 14:47:32.937 [CbsUIHandler]              Terminate:
4076: 2013-01-04 14:47:33.508 [CBS]                       ...done installing 'InkSupport DesktopExperience '. Status: -2147024629 (8007010b)
4076: 2013-01-04 14:47:33.529 [Provider]                  Skipped configuration of 'Ink Support' because install operation failed.
4076: 2013-01-04 14:47:33.543 [Provider]                  Skipped configuration of 'Desktop Experience' because install operation failed.
4076: 2013-01-04 14:47:33.551 [Provider]                  
[STAT] ---- CBS Session Consolidation -----
[STAT] For
          'Ink Support',
          'Desktop Experience'[STAT] installation(s) took '46.1703264' second(s) total.
[STAT] Configuration(s) took '0.0217053' second(s) total.
[STAT] Total time: '46.1920317' second(s).

4076: 2013-01-04 14:47:33.557 [Provider] Error (Id=0) Sync Result - Success: False, RebootRequired: False, Id: 311
4076: 2013-01-04 14:47:33.561 [Provider] Error (Id=0) Sync Message - OperationKind: Install, MessageType: Error, MessageCode: -2147024629, Message: Attempt to install Ink Support failed with error code 0x8007010B., AdditionalMessage: The directory name is invalid
4076: 2013-01-04 14:47:33.566 [Provider] Error (Id=0) Sync Result - Success: False, RebootRequired: False, Id: 35
4076: 2013-01-04 14:47:33.574 [Provider] Error (Id=0) Sync Message - OperationKind: Install, MessageType: Error, MessageCode: -2147024629, Message: Attempt to install Desktop Experience failed with error code 0x8007010B., AdditionalMessage: The directory name is invalid
4076: 2013-01-04 14:47:33.797 [ServerManagerPS]           [STAT] Overall Sync Time: '46.4684482' second(s)
4076: 2013-01-04 14:47:33.821 [ServerManagerPS] Error (Id=0) Installation of [Ink and Handwriting Services] Ink Support failed. Attempt to install Ink Support failed with error code 0x8007010B.  The directory name is invalid
4076: 2013-01-04 14:47:33.848 [ServerManagerPS] Error (Id=0) Installation of [Desktop Experience] Desktop Experience failed. Attempt to install Desktop Experience failed with error code 0x8007010B.  The directory name is invalid

I've run a trace of TrustedInstaller.exe with ProcessMonitor but it shows no failure for a directory search.

Internet searches have not been helpful.

I've spent all day on this problem and have now given up trying to resolve this on my own. I just don't know what directory cannot be found.