Engine dies but car is still on?

I have a 2001 Dodge Intrepid with quite alot of miles
on it. (We're planning on getting a new car soon but
until then, I need the Dodge for commuting to
work.) It ran fine, brakes are great. However, the
check engine light comes on and off occasionally.
Just recently, while driving, the RPM would drop to
0 and the steering wheel would seem to get stiff,
unable for it to turn. The oil light? I think that's what
it is, would come on. We've checked the oil, and it
seemed pretty well. The batteries are fine because I
still able to roll up and down the windows and the
lights and radio come on and off. I would then try
and press the brakes and they seem pretty stiff as
well. Sometimes I can get the car to start up again
after turning off the car. But there are times where
the engine would turn but not start up so I would
have to wait about 5-10min. What is the cause?
With the amount of miles, it wouldnt be worth it to
fix but I would just like to know the problem.