Thanks for the replies. I was finally able to resolve this issue. I made sure that his My Documents was pointing to the default location on the laptop. I had our network admin restore the files from a backup tape. After that I reset the Offline files cache (Folder Options, Offline Files tab, press CTRL+SHIFT then click Delete Files). After the computer restarted I redirected the My Documents back to H:My Documents. Restarted twice to be sure it was synchronizing all of the files. It then worked perfectly.
However, in all of this I also discovered something else about offline files when using GPO in Active Directory. There is a setting in Computer Policy, Network/Offline Files/Synchronize all files before logging off. If this is Not Configured the default is to do a quick synchronization. In order to ensure a full synchronization of all files this policy must be enabled.
Maybe this will help someone else along the way.