Quote:
When close cold water heater valve above heater and let it sit; 15 minutes later; could hear elements clicking, and water did get steaming hot, but when open cold water inlet valve water got cold again,
Whoa! You have just described a bad dip tube, (see image). As you can see by the image the dip tube directs the cold water down to the bottom of the heater where it's heated by the lower element and raises to the top where the upper element maintains it. If the dip tube's shot the cold water will stay in the upper part of the tankand you'll have the exact situation that you describe. I can't believe that nobody's flashed on this eariler.