My 2004 dodge stratus won't steer

Could be as simple as loose power steering belt, or pump beginning to fail.

bad steering lock , change the barrel.

the pump dies when the engine stalls or runs too slow.
so, the steering has nothing to do with that , unless the
pump seized, so drop the belt and start car.
if car will not start, that is a no start question
post it as, cranks fast but will not start. and what engine option
some have diesel.

try rocking he steering wheel back and forth and turning the key at the same time

Sounds like the power steering pump has seized up. The question of whether you can change it yourself depends on your abilities and knowledge of auto mechanics, and having the necessary tools.

You probably have a damaged clockspring assembly. You must remove the steering wheel and partially disassemble the steering column to replace it.

could be low power steering fluid or bad pump

Change belt,its glazed and it squeels when cold and when warm it's OK

Sounds to me that the power steering belt is loose. If it is a 2.4 litre engine it has two serpentine belts. You should replace the belts especially if it was smoking.

You'll need to be able to get the car up pretty high because you'll have to lower the front subframe. First disconnect it from the steering column under the dash,pinch bolt, so you can lower the gear and subframe. Raise car up, You'll need to lower the rear of the frame not the front leaving the gear on the frame. This makes it easer to access the gear bolts and lines. Once lower and everthing is unbolted, you may have to disconnect the lower steering shaft from the gear in order to get it out. It should be a roll pin that you will drive out. Everthing else is straight forward, tie rods etc.The lower shaft is master splined so you won't have worry about getting it on wrong. One caution, don't let the steering wheel turn after column is diconnected. It will damage the clockspring in the upper column later.