You may want to try running this fix from Microsoft: http://support.microsoft.com/mats/Program_Install_and_Uninstall
and uninstall all traces of any versions of Reader. If you want to reinstall Reader, try downloading its full installer from http://get.adobe.com/reader/enterprise/
Thank you for your help. I finally figured out that there must have been a camera attached to the computer at one time, and installations were referencing drive F:\. After using regedit to eliminate all references to that drive, I was allowed to unregister and reregister windows update services, which fixed the problem.
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