Open Web Page in Windows 2008 R2 Task Scheduler runs forever

Sounds like a security\permissions issue related to the creation of the log file to me. Your script isn't breaking so that means that either you're not trapping that error or it is actually creating the log file but the account you're using to look for it doesn't have access although that last possibility seems unlikely.

I think your title is inaccurate- you say that the app does perform the processing tasks so the scheduler is telling the truth and it is executing what you ask it to when required. What's not working is the precise behavior of the script you are running in the security context provided by the scheduler on Win2k8. Have you tried explicitly scheduling it in a particular user context? Simply scheduling a task while logged in as an Administrator will lead to the task being run in System Context which may not do what you expect. There have been changes in this area between W2K3 and W2K8 so it's not surprising (to me at any rate) that something that worked OK on W2K3 would fail on W2K8.

The account used to perform the copy must have the "Restore files and directories" user right to change the owner to anything other than itself or Administrators.

http://technet.microsoft.com/en-us/library/cc783530%28v=ws.10%29.aspx