The Firefox Sync Key (aka Recovery Key) hasn't been used since the Firefox 28 version. All you need is the email address you used when setting up Sync and the password for your Sync account - assuming that you updated your Sync account to a Firefox Account after updating beyond Firefox 28.

And the old "pairing" feature is gone, too.

If we have sync key code, why won't Sync effectively complete sync; so that we recover lost data and passwords?

Jerry,

If you are trying to recover data from an old Sync account, you will need to be using an old version of Firefox - Fx 28 or earlier. Firefox 29-plus versions aren't capable of interfacing with the old Sync service.

Firefox 29 was released on April 29, 2014 - almost 8 months ago. If you have been using a Firefox 29-plus version, you wouldn't have been using the old Sync service anyways. Your old Sync Key isn't needed with the newer version; as I mentioned above, all you need is the email address you used for Sync and the Password - unchanged from the last time a "Sync" was done with the missing device.

Any further questions should be posted in a new question thread. https://support.mozilla.org/en-US/questions/new