Current Firefox releases no longer use signons.sqlite but now use logins.json to store the passwords. the key3.db file that stores the encryption key hasn't changed.

Does the logins.json file has any password entries?

You can open the file in the Scratchpad ("3-bar" menu button or Tools > Web Developer). Click the "Pretty Print" button to format the file for readability.

In the event that the passwords information is lost, you should record all information in a separate text file somewhere else on your hard drive, or written down. You can easily copy and paste if you need to do so. If you are concerned about someone else looking at that file, you can compress it using a password.

These can't get your data back, but will help in the future.

These add-ons can be a great help by backing up and restoring Firefox

FEBE (Firefox Environment Backup Extension) {web link} FEBE allows you to quickly and easily backup your Firefox extensions, history, passwords, and more. In fact, it goes beyond just backing up -- It will actually rebuild your saved files individually into installable .xpi files. It will also make backups of files that you choose.

OPIE {web link} Import/Export extension preferences