Without seeing a Safari crash report it's difficult to say exactly what's causing Safari to quit.
Try troubleshooting third party add ons > Safari: Unsupported third-party add-ons may cause Safari to unexpectedly quit or have performance issues
How much free space on the startup disk?
Right or control click the MacintoshHD icon. Click Get Info. In the Get Info window you will see Capacity and Available. Make sure there's a minimum of 15% free disk space.
If you haven't done so, run Disk Utillity in case the startup disk needs repairing > Using Disk Utility to verify or repair disks
Keep in mind a Mac running Panther has a much older version of Safari which may have problems accessing certain features on the web.
I'm not sure how much free space he has, would have to check, but I cannot imagine the disk is anywhere near capacity. There are no third party add-ons that I know about, and I've already repaired permissions. I think your last point may be the most appropriate - the OS needs to be upgraded. But I still recall the nightmare of installing Tiger when it first arrived, and as I'd have to do this for him (he's not very computer literate) I can see a few frustrating days ahead of me. Maybe I can talk him into just buying an iPad instead?
The iPad requirements:
- Mac computer with USB 2.0 port
- Mac OS X v10.5.8 or later - Leopard
- iTunes 10.2 or later recommended
(free download from www.itunes.com/download)
- iTunes Store account
- Internet access
Or, without a computer he would need a Wi-Fi network using iCloud to backup and restore an iPad > Apple - iOS 5 - See new features included in iOS 5.
Check to see if his Mac can run Tiger > Mac OS X 10.4: System requirements