Found at the back of the refrigerator today:
Oops. Thankfully not the end of the world, but I've rediscovered my zeal for the little things and the infinitesimal difference they make in the grander scheme. It's the principle that counts. An attitude of thrift at the limp broccoli level will reinforce my attitude of thrift at all the other levels. I aim to manage my fridge better this week, prevention is worth a pound of cure after all.
I've had success with reviving tired celery in the past, as well as potatoes, parsnips and carrots, by placing them in cold water in the fridge (it works better than leaving them out on the side for some reason I don't understand). So I trimmed a sliver off of the dried out ends of the broccoli stems and placed them in a jar of cold water in the fridge.
An hour later:
Perky and crisp enough to chop up into pasta.