Engine made a weird noise when i started it & then the power steeing did not work & the battery light came on

Assuming you know how to test automotive electrical circuit's ,test main power (battery + voltage ) & negative grounds ? Voltage drop test PCM power an grounds . check battery voltage , charging (alternator ) system .
Charging System Problem Voltage Drops
Electric Testing Techniques You Need to Know

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Mastering Voltage Drop Testing with Pete Meier and Jerry Truglia

PCM power and ground testing avi

50-60 psi is not enough. you want 130+

Darn, just sold my '95 neon. I never had to bother with the electronics, it always worked. That da da noise sounds like must come from some relay. Come to think of it, Chrysler makes had a kind of "main relay" called the Auto Shutdown Relay or ASD relay. It's purpose was as a main relay for sending power to necessary things to keep the engine running-like power to the ignition coil, and power to the fuel injectors, and to the fuel pump. This relay is triggered or controlled by the computer.
If you have a relay chattering and it is not a bad relay, then could also be a poor positive battery connection, or even a poor ground too. If that chattering sound is from the starter solenoid (on the starter motor), then you either have a weak battery or a poor connection ... or a bad solenoid.

the clicking noise was due to the bad battery. the starter solinoid was not getting enough power to turn it over. try this if possible, engine off at battery should be at least 12.6 volts. start the car and if alternator is ok, it should read 14.2 to 14.7. if not repair alternator. what happens, is the voltage regulator in alt. goes bad and will not supply enough current to battery. good-day !

get to your mechanic. its probably some conponent were not put in place properly

You said you checked your battery, did you check volts and amps? It's possible that your battery is not functioning properly. You may need a new one. Does it start if you try to jumpstart it?

Most likely problem is a low battery. Clicking noise is starter trying to engage.

check you battery and battery cables...sounds like a big voltage drop

i had the same exact problem with my chevy s-10, but once i replaced the battery it ran fine no problem, u may have fried some circuits and relays while jumping the car, and alot of times that clicking noise is your relay burning out, did your car start doing weird things too? like ejecting cd's, flashing lights really fast and weird noises?