A couple of possible causes. It may be caused by an add-on, to find out if that is the case follow the procedure in the troubleshooting extensions and themes article. Another possible cause is the file that stores history and bookmarks is damaged, for details on fixing that see http://kb.mozillazine.org/Locked_or_damaged_places.sqlite

Thank you, TonyE, much appreciated! In the meantime, I've switched to Safari, which works well, as I'm quite unversed in technical matters of this kind.

I actually upgraded to Mozilla's latest version, thinking that might fix the problem, but no...still no URL. I'll try to do the troubleshooting you recommend or get someone more competent than myself to do it.

Thank you!