Jarkman ~
What you are seeing, the box with the 4 languages, is indeed a kernel panic.
Go to /Applications/Utilities/Console and check your logs for anything revealing.
Alternatively (or if your console doesn't launch), you can tail your logs in terminal;i.e.
tail -f /Library/Logs/panic.log
"tail" to see the last part of your logs, "head" to see the first part, and "cat" to see the entire log.
Your logs all reside in /var/log & /Library/Logs & ~/Library/Logs
Reinstalling the COMBO updater for 10.3.7 may help. Remember to repair permissions both before and after installing the combo updater.
Beyond that, you can do an archive/install of panther without losing any information.
Good luck =)