Try booting into Safe Mode (takes longer than usual). If still no keyboard function, back to Recovery Mode to re-install system.
If the keyboard works in Safe Mode, you might have some interfering apps, tools or drivers installed that "kill" your keyboard. Delete those completely without traces, then reboot regularly and let us know if solved.
My letters/numbers keys do not work, but my function keys work, so I can't log-in in the appropriate field. I can move the icon with the mouse, (bluetooth or USB) I've tried 2 keyboards, one USB the other Bluetooth, but I can't get past the log in screen cos the letters & numbers don't respond. I can adjust the brightness using F1 & F2, and I can adjust the volume with F11 & F12.
Luckily I have this MacBook Air!
It started off as a hardware issue where I couldn't even start up. Also I can't get a hardware test to run to completion (you know, switch on whilst pressing D). Strange that the D key works for this! In a PRAM reset Option/Command/R/P seem to work; but I get stuck at log-in, no letter/number recognition. Safe Boot (start-up with Shift key on sound) doesn't fix anything, and can set me back to square one. Luckily I'm back to the most advanced; in a position to log-in, but unable to effect the letter/number keys! I think this is a big issue guys!
Any ideas anyone?