What do you mean by not start? It cranks but won't turn over, or it doesn't even crank? I have a 97 Sahara Automatic and a couple of weeks ago in this bitter cold, I left the interior lights on in my Jeep by accident and since it's not my daily driver, it sat like that for a couple of days. About 4 days later when I went to take the Jeep the battery was stone cold dead. I mean not even a dash light or any beeps or any indicator lights at all came on, it's as if I didn't even have a battery. So I charged up the battery for the day and went to start it later. It would crank but not turn over.
I finally got it to turn over by giving it gas while cranking but I had to keep the gas pressed in order for it to keep running and it would die as soon as I let off the pedal. The engine was rough sounding as well like it just wanted to stall.
Now here's the weird thing, I was going to move it into the garage so I can work on it and see what's wrong, so I kept it rev'd up and put it into drive. As soon as I put in drive, the idle went normal and the Jeep behaved perfectly like nothing was wrong. No more engine stutter or rough idle and it's been fine ever since. A couple of days later the check engine light came on and it was throwing the code (I forget the number) but it was for "battery disconnected recently." I'm assuming it was because my battery was so drained, that it may as well been disconnected.
The engine light went away after a day and everything stayed fine as normal. So I don't know if there's any truth to it, but my 97 had a hell of a time starting after a dead battery