You should indeed be able to export your certificate on your home Mac !
The first thing to do would be to perform a few maintenance and optimization tasks in order to make sure that no minor disk error or permissions issue could prevent Mac OS X from running normally. In order to do so, follow these steps :
• Boot from the Panther Install CD 1
• Use the Installer menu in order to open the "Disk Utility"
• Click on the "First Aid" tab and repair the hard drive
• Restart your computer
• Use the "Disk Utility" located in your "Utilities" folder to repair the permissions on the Mac OS X partition
Then, you may want to clean-install Mozilla or reset the contents of your certificates manager. Indeed, it is possible that this component is corrupted and therefore unable to store certificates normally.
Finally, make sure that nothing could prevent the browsers from processing the information normally — turning some features off, for example.
Let me know if this helps !