I think it may well be one of the cables for the keyboard and trackpad. If the cable seemed broken when you ordered the replacement part, then it very well could have caused the keyboard backlight to break too, as they could be shared from the same cable. You might also want to check all other cables to make sure that the keyboard cable is looking fine.
If the replacement cable does not fix these issues, the the problem may well be something else.
Good luck fixing your MacBook Air!