Keyboard does not work or light up
Could these two flex cables be the culprit?821-2697-A (Keyboard Backlight) 821-00507-03 (IPD)

Yes, they could be the culprit.
Are they, however?  Who knows.  You have to do proper diagnostics to determine what is wrong.  Simply looking at something is just guessing.

Could replacing keyboard backlight flex fix my keyboard problem?

Possibly, if it is what's causing the issue.
You have to test the cables - that means checking continuity and resistance on each pin.  It can also be the keyboard controller.  It can be any number of things and only putting hands-on and doing actual diagnostics can you be certain.
It's understandable that you want some more certainty than guessing, but unless it's blatantly obvious like the cable is burnt or cut, nobody can simply look at a picture of an electrical component and tell you proof positive that it's the failure point.  If it were obvious, you wouldn't need to ask.