The fix, to install modules from the VirtualBox ISO, is detailed by Pavel at the following link:
Failed to start light display manager? - Community - Parrot Community:
When you obtain the failure message about lightdm, simply press ALT+F1 and log in there. then:
- sudo apt-get update
- sudo apt-get upgrade
- sudo apt-get install build-essential module-assistant
- sudo m-a prepare
- mount /media/cdrom
- sudo sh /media/cdrom/VBoxLinuxAdditions.run