I tried several times to use the old backup, no dice.
I could mount it, and chose it in the TM preference pane, but it wouldn't bring up any history, and upon backup, it would start from scratch.
*sigh*
I kept the old backup, and started a new complete backup.
Fortunately, it was only my wife's machine, which doesn't hold all the important data.
If it had been my iMac, I'd been super pissed.
-t