After replacing the battery the engine will not stay running?

Thank you so much for answering! Yes, it stalled a few times before the new battery. Started happening end of summer Aug-Sept. We are in Arizona very hot (the battery wasn't "dead" bad, but we figured it was part of problem and this is why we replaced it) After new battery, we drove to Disneyland and back with no problems at all. The link you sent makes so much sense! We are going to replace this sensor. I'll let you know if it fixes the problem in a couple days. Thanks again so very much!

Well, we changed out the crankshaft sensor and it seemed to work. However, when we went to road test it, as soon as he hit the gas to speed it up it shut off. It started right away, went a few feet, then shut off again. Then it would start, shut off, start shut off then didn't want to start at all. Had to push it back home. G was driving, I was passenger and to me, it felt like it wasn't getting gas when it shut off the first time, like it couldn't handle the pedal to metal acceleration. No lights came on. Battery still good. Because we haven't been able to drive it anywhere, we can't get any codes to come up either. Guess we should probably check the fuel pump? Or have you heard of this problem needing something else? Any help is appreciated.

Starting to wonder if it's something that shuts it down when warmed as well. We'll test the fuel system in the next few days. Thanks for the link, we'll keep you in the loop.
Garrett