How do I disable my computer's HDD LED?

TL;DR Tape over it.

Disregarding whether that's a good idea or not*, the easiest way to 'disable' the LED is most likely to open up your laptop case and unplug the LED ribbon cable. Barring that as a possibility, the next most practical solution would be place tape (or an aesthetically pleasing sticker) over the LED.

While it may be theoretically possible to modify chip firmware somewhere on your motherboard to disable the LED, there won't be any easy way to do so in a software setting expressly because the engineers designing computers, for various reasons* believe that to be a bad idea.

*_{^{See e.g. http://forum.notebookreview.com/threads/how-to-disable-the-hard-drive-led-through-windows.239562/page-2#post-3236374}}