I would start with checking the battery (have it load tested) many auto parts places will do it for free, as well as sears or any battery shop.I have done both. Have had it Towed and also tried to start it for 20 min by pushing the push start repeatedly. Eventually it started after 15 min of pushing the push start button repeatedly. When it does not start, the first push of start button makes the dash come on normaly. Second push everything turns off. When it acts up like this, i did notice the horn will not beep when the key fob is pushed 2x to lock vehicle. And I also noticed, i went to open the back hatch, which opend fine (from pushing the hatch latch button itself (not the key fob). But when I went to close the hatch by pressing the button on the inside of the hatch, it would not close as if there was no power.. I had to manually pull it down to close. Not sure if that means anything but I figure at this point, anything out of the ordinary I should mention.
if the battery checks out, then have the battery cables looked at or checked, they can ohm check the cables and do a voltage drop test. the battery cables can do weird things even based on the ambient temperature if they are no good, also the battery cables have been known to corrode on the inside and look fine on the outside, not saying this is the case here but it should be noted. if it drives normal and operates normal other than those problems mentioned I would lean towards it being a power problem. maybe a bad ground. that's where I would start.
on my 2012 one of the signs of having low power I have noticed is the rear hatch will not close properly, that may not mean anything here but it is one thing I have noticed, these trucks are real finicky when the voltage is low and will do all kinds of weird stuff.