OK, got it figured out. What everyone said was dead on.
The problem was a loose nut on a bolt that holds the battery positive cable lead and the starter cable lead together. We checked the voltage there first and it was 12V - wouldn't start. (Scratch head) We then were able to jump it and it started. (Scratched head some more). While we were watching it run, I noted some smoke coming from this bolt holding the leads together. We wiggled the cable and the car died. With the engine dead, we wiggled the cables more and the lights would dim. (I assume the smoke was coming from the bolt that was heating up and melting the plastic around it.) Turn the key, and it started again.
There was a lot of wiggle room between the two leads. So, much that a bump in the road could stop the connection making the car shut down while driving. We were not able to tighten the nut down anymore, so we put 2-3 washers between the nut and the leads. With everything tightened down, no more play and no more care car shutting down and this time it would start too. We test drove it around for 3-5 miles go over bumpy roads too, and it never missed a lick.
Thanks y'all for your help. You saved my Dad some money.