Dell seems to have more keyboard issues then Lenovo, at least in my experience with the E6540 - granted my E6440 was fine with the original keyboard before I did the keyboard/palmrest swap, but it does happen on these more then some other brands. That said, check if the numlock key is dead [lock with 9 as the “key”], or not active - sometimes you get lucky.
The DP/N is 564JN [US English Backlit] or M8F00 [US Engligh non-backlit]. With this machine, you can often find the backlit version for a few bucks more. All you have to do is transfer the flex cable since this isn’t tied to something like the motherboard to upgrade the keyboard type on these machines, which is a variable on the E7’s to the point I prefer to seek out a backlit spec machine unless I know it can be done. I did it on my E6440 because it originally shipped with the E5 non-backlight single input keyboard, and it worked fine. The machine accepted the keyboard like it was shipped that way even though I added it on 6 months into my ownership. The only “clue” is within the system configuration that my setup is not original - but then again, neither is the LCD - went to HD+ when the base HD panel had issues.