Did you use the Sync service? If your old computer is not available to authorize the new computer, you need the recovery key that should have been displayed during the sign-up process. See:

https://support.mozilla.org/en-US/kb/share-bookmarks-tabs-and-more-your-other-computers#w_what-if-im-not-near-my-first-computer

Hopefully that wasn't saved only on the computer that died...

Do you have any backups from your old computer?

Yes, everything (except passwords) is backed up using Sync. I'm sure you used to be able to log into Mozilla and download from there; is that no longer possible? If it isn't, then I do have backups, but what am I restoring (and where is it in the folder structure)?

I don't use Sync myself. If the steps in the article don't work, then the backup probably is the best source.

There are two files in your backup that could be useful:

• places.sqlite - database file containing bookmarks and history
• bookmarks-2013-02-20.json - latest dated bookmark backup file

If you want all the history, you could track down the first file and drop it into your newly created settings folder. If you only want the bookmarks, you can "restore" the old .json file to your new PC. Both of these will wipe out any bookmarks you have added on the new PC. If you need to preserve those, there is a way. (To avoid doubling the length of this post, I'll spare you unless it's relevant.)

For a recent discussion of how to track down the files and get them over, see this recent thread and related article:

• restore bookmarks from vista
• Restore bookmarks from backup or move them to another computer

I've finally managed to get access to the offending laptop. It's amazing how much damaged little splash of beer can do!!!

Using Firefox Sync, I've restored the most recently dated backups of bookmarks (and exported them to an html file on an external drive, in case this saga hasn't finished yet). Unfortunately, I've lost everything else (tabs open, history, etc).

I'm certain I saved a copy of the "recovery key", but can't find it. Why does Firefox Sync use a recovery key, rather than allowing you to recover things by logging onto a website? I understand the need for exceptional caution with passwords (but most of us use LastPass or similar for that), but it's gross overengineering for bookmarks etc. And, the result is, that if you lose the recovery key then you might as well not have bothered!

Maybe I'm using the wrong product? Any ideas?

Anyway, Jefferson, thank you very much for helping me recover from this.