Create another user account on your computer, log into it, start Opera and see if the jumplist works there. If so, find its file in its AutomaticDestinations and copy it over to yours. Then, you can delete that user account.
If you get your tasks but "open new window" still points to the wrong opera.exe, you might have to edit the file (with a hex editor or something).
Another thing I was thinking of if that doesn't work is to uninstall Opera, delete its program files folder, remove the Opera software profile folders in Roaming and Local Appdata and remove all traces of Opera from the registry. Hopefully that won't be needed.
