Mustang no crank no start

I recently purchased a 2001 mustang gt and owner
showed me battery light goes on and off when I first
got it.After about a month now of driving today the
car started smoking and smelled rich of oil and shut
off completely.When I put the keys in the lights and
radio come on but when I click over to try and
crank all power goes off and doesn’t make a sound
and no crank I’m confused on where to start
looking for the problem.I checked all fluids and
everything is good and car did not leak anything
when it shut off.