Today the power steering on my car gave out then the battery died. I bought a new battery and the car started right up. When I went for a test drive, the power steering still wasn't working and then the car died after driving it. I got it to start up again, but whenever I turned on the lights, the car started dying again. What do I need to replace? I was thinking it might be the serpentine belt.

Can someone scan it for codes ? Pending codes may not set a light .

hard to steer and battery light on sounds like a broken belt

Check for fuses or fused link, also check for voltage regulators, Chrysler uses an integrated power management system that is under the fuse panel in the engine compartment.

I would start with a cylinder compression test to find out the engine's internal mechanical condition. If compression is good on all four cylinders, it should be good to put whatever new parts it needs to run right. All new parts won't help if you have an internal problem (like a bad head gasket, or valve train problem). That will have to be fixed first. Don't throw money on new parts until you know you have a good engine.
Is this a carbureted engine? If it is, you may need the carb rebuilt.

Check all fuses ,wiring anywhere short or check alternatour

Look for a light on the dash that says SECURITY after it doesn't start. These cars and many more GM's have had problems with the antitheft system. Parts in the system tend to fail and cause this "no start" situation. Symptoms range from stalling while driving, to starting for 1-5 seconds and then stalling. This link might help you if this ends up being your problem.
http://vatspasslockpasskeysecurityhelp.yolasite.com/

your altenator is bad, and it is traning you battery.

yes you will need to replace the belt before you drive anywhere.

if your battery died while driving and the car cut off while your driving,, your problem is from your alternator!!!,, on a normal working car, you can start, remove ther battery terminals and the car would still run cause the alternator will be powering the car. In your case the alternator isnt working and the car was working on battery power therefore when the battery went dead the car cut off.. Your alternator need \s to be charging between 13.5 and 14.2 volts.. as little as 10 volts will keep the vehicle running.. I'd suggest you have the alternator replaced.