Photoshop Elements 4.0 unexpectedly quits when launching

Question

I just installed Photoshop Elements 4.0. Every time I try to launch the program it starts to open and then unexpectedly quits and gives me the option of reporting it to Apple. I've installed it four times and this happens each time I try to launch the program. The installation goes fine as far as I can tell and I restart the computer each time.
I am running OS 10.3.9 on a PowerPC G4 with 640 MB of RAM and 108 GB available on the hard drive, so there shouldn't be a problem with meeting the System Requirements.
Power Mac G4, iBook G3, Mac Mini   Mac OS X (10.3.9)  

Answer 1

After reading your response, I think I repaired permissions (in Disk Utility, right? Click on the disk and then on Repair Permissions). I tried several more installs, repairing permissions before each one. That didn't work, so I created a new administrative account and tried installing from there. I did that a couple of times, again repairing permissions before each one. PE still crashes when launching.
My computer is on 24/7, with a backup to my external hard drive scheduled for each night. Since I first installed PE, my back up software has also been unexpectedly quitting. I did a backup after completely shutting down my computer and it worked fine. Won't know until tomorrow whether the automatic backup will work.
I checked the Adobe support for PE and tried some of their suggestions, including going to Console to identify software conflicts. I didn't find anything there, except that the crash log says it's a kern problem. Does that help at all?
I've never had a problem with installing software before. Should I erase my disk and reinstall everything, or is that a last resort?
Power Mac G4, iBook G3, Mac Mini   Mac OS X (10.3.9)