Why there is not a moodle/mod/attendance folder in the download file provided for version 1.4?
Because Attendance is not a standard module yet. If you look at the modules page, you'll see it's labelled as 'unstable' (= use at your own risk 
)
But now I am afraid I have old versions of these files mixed with the new version.
Don't use the files from the backup of your old installation. Instead, download the 1.4.x version of the module (available from the modules page). Remember to visit the admin page to make sure the database upgrade is done.
Hope this helps,
Przemek