You're talking about two very different functions.
While you could reprogram the key to perform a different function (which you should NOT do), you can not reprogram the LED to light on different actions. That is hardwired into the circuity of the laptop.
If the LED does not work properly, your only option is to take it to a laptop repair facility to see if then can figure it out. HP does not do these kind of repairs, so you would have to seek elsewhere.
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