Even with a NEW BATTERY,STARTER,still having issues starting;WHY

MEINEKE checked the battery,but to be fair,the battery was @least 3 or 4 years old.As for the starter,Firestone checked it and it was a re-bult starter from Sears,and I work for them,that's why it's stranged that the starter was bad.Brought it last year.That neutral safety switch was done over 5-6 years ago,so does it ever go bad with time? What about the back-up lights in why it willn't work even with NEW BULBS?And the turn singles,turning right it just clicks off about 1/4 of a turn of the wheel?That was done by Meineke also.

ok,you took the old key and had a new key made.did who ever made the key put the correct resistance chip to the new key?. old key still starts the car?