Do you have a folder called 'prj' in the same directory as the .qvw file?
If so, delete that folder. You will be able to open the file then with your PE version of QV. Somehow, QlikView automatically generates those folders, indicating it uses version control for the file. QVW files under version control, can only be opened with licensed versions of QlikView. By deleting the prj folder, you disable the version control for that file.