One suggestion. Try trashing the com.apple.dock.plist
Follow this path: Macintosh HD>User>Library>Preferences>com.apple.dock.plist
Drag the file to the Trash, empty the Trash and reboot. Might be a corrupted preference file causing the problem. Also, I have never added a .dmg to my Dock before but I just tried and discovered it will ONLY take a .dmg file on the right side of the divider, not the left side where all your programs and applications are. Seems to me if you get the message that there are "no mountable system files"... the Dock preference file might be corrupted and can't "see" the .dmg files. Anyway, try my suggestion and let us know how it goes. I'm anxious to see if this fix helps. As for
<<a number of programs have stopped working; iPhoto, iMovie, Internet Explorer, Script>> your programs you listed not working, I would find the .plist file for all of those programs and do the same thing. Trash their preference plist file, empty the Trash and reboot. Also, Repairing Permissions cures a lot of ills on a Mac. Try that also. Applications>Utility>Disk Utility Highlight the MacintoshHD on the left and click Repair Permissions below.
Don't ya just "love macs"...