It randomly won't crank
No, has nothing to do with starting the car. Check your battery cables and terminals for corrosion.
Tom is correct, the fob battery won't cause your problem, do what he suggests and double check the shifter, make sure it is in the park position and the indicator shows that it is in park, have seen a few of these park switches get out of adjustment or just go bad.
Search Chevrolet Silverado 1500 Questions
Chevrolet Silverado 1500 Experts