Dell latitude 3420 keyboard backlight not working

Does the keyboard you purchased have the backlight option?  Both standard and backlit keyboards are available for this model.

If it is backlit, did you plug in the backlight cable when you changed the palmrest assembly?

@ejn63​ I have the Dell latitude 3420 with the non backlit keyboard, will the backlit keyboard be compatible with my laptop?

It should be yes -- but you need a complete palmrest assembly, not just the keyboard.

https://www.parts-people.com/index.php?action=category&id=140&subid=1537&refine=keyboard

The procedure for replacing the part is not trivial -- only you can assess whether the job is within your skill set.  The entire system has to be completely disassembled as detailed in the service manual.

https://www.dell.com/support/home/en-us/product-support/product/latitude-14-3420-laptop/docs