When installing the updates to Joomla 3.4.x you may get a popup dialog box message indicating an "Invalid Login". After clicking the OK button the update process will appear as if it is still updating but the progress bar will not move. In this case the update has failed and no change was made to the system.
We found a number of reports of this issue and what we found was that it is most likely a permissions issue on the folder structure where Joomla is installed. By resetting the folder and file permissions so that the web server had complete control of everything, the update competed normally.