Certain Lenovo Function Keys Not Working: Solved
The Short Answer
For me, this turned out to be a hardware problem. The solution was to replace the keyboard.
Background
I have a Lenovo ThinkPad P1 Gen 3 laptop, and I use a ThinkPad Wired USB Keyboard with TrackPoint so that I can elevate my laptop on a stand while having a keyboard on the surface of my desk.
Some months ago, certain function (Fn) keys stopped working, on both the laptop keyboard and the attached USB keyboard. So I knew it was a software issue, not a hardware problem with the keys. I tried updating drivers, rebooting, detaching the USB keyboard — all the usual stuff. I updated BIOS, just in case. Nothing helped, and I eventually gave up on being able to use those function keys.
This was super frustrating. My F5 key didn't work, for example, but my F6 key did. The Lenovo hotkeys for decreasing brightness and increasing brightness are tied to F5 and F6 respectively, so I was able to increase the brightness of my screen with a hotkey, but to decrease brightness I had to open the Windows "Change brightness level" UI.
One day, I randomly decided to toggle function lock (FnLk) on my USB keyboard, by pressing Fn + Esc. The onscreen indicator confirmed that function lock was enabled. I noticed that the function lock light was not lit up on my laptop keyboard, so I used Fn + Esc on my laptop keyboard to toggle function lock, and again made sure that it was enabled.
Weirdly, this fixed my problem on my USB keyboard, and I was able to use all my function keys again. But my laptop keyboard continued to have problems, which eventually got worse. My Tab and Backspace keys started failing intermittently, and I found that if I mashed them just so, they would work. Perhaps I had originally had a software problem, but now I definitely had a hardware problem. My 'T' and 'Y' keys started failing soon thereafter.
I tried popping off keys, hoping I'd find some sand or cat fur or something obstructing the keys. No obstructions were apparent. I finally decided to bit the bullet and replace the keyboard.
Keyboard replacement on a P1 Gen 3 is an expensive and time-consuming undertaking. You have to take apart the entire laptop in order to remove the keyboard. It's not like many other ThinkPads I've had, where you could use a special tool to release the keyboard and lift it out from above. Instead, it's "plastic-soldered" to the shell of the keyboard, and the recommended approach is to replace the top half of the shell and the keyboard together, as one integrated component. Lenovo's official replacement for "C-Cover with keyboard, English, Backlight" is over $230. Fortunately, I was able to find a cheaper alternative on eBay: "OEM Lenovo ThinkPad P1 Gen 3 Top Cover Palmrest Keyboard Touchpad SN20W85532", for under $80, which appears to be in perfect condition. After watching a video on how to perform the replacement for a X1 Gen 3, which is the same process, I decided it was too fussy, and that I would be better off hiring a pro to do it for me. It took him under an hour, and so far I'm delighted with the results. My laptop feels like new.