At the midpoint of the season, I am using the traditional game 8. The Cowboys went 3-4 (they had a bye week). After week 9 they were 3-5 (loss to Atlanta).
At that point, there was a mathematical shot at the first pick in the draft had Dallas continued to lose. They would have ended up 3-14, which would have given them the top pick. There were also other points in which it was mathematically possible. Then, as the season progressed, it became mathematically impossible.
At the week 8 point the Panthers were 1-7. The Pats were 2-6. At week 9 the Pats were 2-7 and the Panthers were also 2-7, this would be when Dallas was 3-5.
Dallas was not far behind at 3-5. Dallas didn't play the Panthers until Week 15.
So obviously there was a shot.