xj headaches

ok, heres my problem.
my xj wont start on its own.
i have to jump start it.
i tried this today and when i took the cables off it stayed running.
so i took it for a little run in my backyard and about 200 yds it shut off.
oh yea, the buzzer that sounds when you open the door kept running,
even while i was driving.
then when the buzzer went off the jeep shut off right after.
anyone know what ithe problem could be?
i am no good with electrical stuff.

Remove the battery cables and clean them.

X2... had the same thing happen to me. Couldn't figure it out, til I cleaned off the corroded battery cables. Make sure you get them totally clean and snug them down properly.

Could also be a blown alternator. They don't like battery cables coming loose while running! (It can even fry the computer and any lights that are on if you take the battery cable off while running. 2 things REALLY bad for electronics are too much power and too little!)