"It's telling me that if I run fsck on mounted filesystems it can cause major damage - how do I
You are obviously missing parts of /usr/lib. Maybe fsck can find the missing files and reattach them to the filesystem. You cannot run fsck against a mounted filesystem (actually you can but fsck can make mistakes when you do so).
To run fsck:
Boot your Mandrake install CD and go into rescue mode. Get a command prompt and then run fsck against all of your Mandrake partitions except swap. It is very important that you tell fsck what filesystem type each partition is. fsck can autodetect the filesystem type but if the filesystem is screwed up to where fsck detects the filesystem incorrectly then fsck will really screw things up. So, assuming that you want to check /dev/hda1 and it is an ext3 filesystem, then run this command from rescue mode:
fsck -t ext3 /dev/hda1
Answer y to anything that fsck asks you.
Then do the next partition, etc.
As a side note, whenever I have a system crash I immediately use my LifeBoat rescue CD to fsck 11 of my 12 partitions before I attempt to reboot Fedora.
Checking your lists of files for libgal, libgtk, and libqtmcop against mine you are missing files in all three areas. Which ones are missing is not that important right now. Keep your lists handy and after you run fsck use find again to check your new lists and see if fsck improved things any.
Also check the lost+found directory on each partition to see if fsck placed any lost files or file fragments that it did not know what to do with in lost+found.
Be prepared. Create a LifeBoat CD.