The only other ideas I have are:
You could reinstall the Sunbird application, though this may not do much since this happens on two different machines.
You could check in Synaptic, right-clicking on the Sunbird package to see if in the properties there might possibly be a previous version available.
As well, if you run the Sunbird application from the terminal, there may be some messages listed. That might help in focusing further research. Those messages can then be used in Googling up to see if others have similar issues.
Not sure if any of this will stick to the wall, but I am throwing it out just in case. Perhaps someone else who uses KDE and Sunbird might add to this thread. Good luck.