when you say it started like a dead battery do you mean the starter spun slowly? if thats the case pull the battery terminals off and clean them with a wire brush, if its the original battery or you dont know the last time it was changed it might just be time for a new one. test the voltage of the battery with the jeep off, should be between 11-12v then get the jeep running and warm to the point that it doesnt stall and take a volt meter to the battery again, should be 13-14ish. if its below 11 cold you need a new battery, if its below 13 running you need an alternator, if its above 15 running chances are the battery terminals are dirty. if battery checks out good try "priming" the fuel pump a few times before you start it, meaning turn the key to "on" sit for a few seconds then off then on again for a few seconds then start. jeeps have a check vavle in the fuel system that likes to fail and let the fuel drain out of the lines back into the tank, priming the pump a few times refills the lines and lets the jeep start normally. some people just live with a failed check vavle since it is in the tank but the good news is that its only 5 bolts and 3 hoses to disconnect to drop the tank, takes all of 5-10 min.
also cold stalling can be a sign of a vacuum leak, i cant really offer much help with finding it because i really need the jeep in front of me but the intake manifold gaskets are pretty well known to fail, cant see them being cheap at a shop but its really not that hard of a job to diy but does take some mechanical skill.
check the battery and fuel pump and get back to us.