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Hello Doctor H...
The Driver reinstall was a long shot.
Thinking about this, LED mechanism may not even be in the driver. The two things are not necessarily connected.
I found another post on this same subject, equally frustrating - no solution posted / verified. 
I am not HP support, sad to say.
I want you to call HP on this one.
Last Option:
It is possible the mechanism is in the BIOS and that force flashing the BIOS might kick the LED... that is, if the hardware is still viable: Force flashing (updating) the BIOS might work if the light has not failed, the connection is good, and something else has not faulted.
I hate things that work and then do not.
I will keep looking. If I find a software solution, I will post it.
NOTE .. If you do call HP and they tell you the mechanism IS in the driver and not matter WHAT you do you cannot get this 15.3.x driver to work - you can go to the Synaptics website and download and install the Synaptics driver. It comes in all flavors (all Windows) and it works. It has all the fancy bits (all the scrolls, and options, and features)... I'll post if you like.
Good Luck!
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