Hello, May I (if you don't mind) suggest that you take a magnifying glass with a lot of good light and look directly at the very end of the two cables from each unit. What you want to do here is to look at the contact tips at the end of each cable ribbon (don't do a lot of bending with them). If you see where there appears to be a missing contact strip at the end then that will be your problem.
The mouse/trackpad will work independently from the keyboard functions. All other suggestions that you've already received are very valid suggestions and like in anything else when trying to solve problems, always start with the simplest one first and then proceed from there. Hope this helps.