2002 Ford Taurus 2002 Taurus Starting problem

For about 3 weeks now I have been having an issue with my car having no turn over when the key is turned. I started noticing the problem intermittently (car would start when cold) when I would drive a short distance to the store and when I would leave the car would not crank at all. The car has the under the dash security system installed that when the key is removed the car will not crank, so I assumed I was having an issue with it. Long story short, I spoke with Ford, ran a bypass which did not help, thought maybe it was heat with the relays or positive cable to starter (both replaced), I took it to Ford 2 times who said it could be the started (have replaced 2 times), had the battery tested (good), and replaced the neutral safety switch for good measure. All of that and no dice. Yesterday I noticed if I rock the car a bit it seems like it tries to fire; I get a slight crank and sometimes griding from the starter. I need help please. Thank you.