Can you be a little more specific? Do you just want to store the packages for KDE 3.4 on the drive, or install KDE 3.4 on a distro already installed on the drive?
 
What distro and version are you using?

(2nd attempt: Somehow pressed return and the form was gone; so if this post appears twice, I apologize in advance).
 
howdy cheetahman,
 
you can install KDE to wahtever directory you want. This also includes folders on external drives. Prerequisite is of course that you have a fixed mount point for the KDE dir on the external drive. I suggest a preocedure as follows ...
 
1) Install KDE to fixed hard disk
KDE will likely go into "/opt/kde" or somewhere underneath "/usr" (distro dependant) and see if everything is running smoothly.
 
2) Leave X and go to console (also make yourself "root") and copy the complete KDE folder to your external drive
(e.g. "mv /opt/kde /mnt/myexternaldrive_kde_dir")
 
3) Create a sym-link to the folder on your external drive
("ln -s /mnt/myexternaldrive_kde_dir /opt/kde")
 
DONE
 
This way the link redirects everything to the external harddrive and KDE still thinks it has set up camp in "/opt/kde"
 
You can also skip the symbolic link. In this case you would have to adjust the evironment vars "KDEDIR" and "LD_LIBRARY_PATH" to tell KDE where its home is.
 
hope this helps

addendum:
 
Just checked the KDE site and they have a nice explanation of things (except the question "How many stars are in the sky?" here ...
 
KDE Faq
 
Chapters 4.9 and 4.13 repsectively address your issue.