I have a 2001 PT Cruiser. The battery light came

BODY CONTROLL MODUALE

I would want to know what the trouble codes are in the computer since the check engine light is on.
Those codes would help you or a mechanic know where to start checking.
If the alternator is not charging the battery, and you know for a fact the battery and alternator are ok, the problem could be a fuse or fuseable link wire, or the computer.

Well the battery light means the battery is not being charged, but it could be a fuseable link or computer problem. Could even be a problem with the ignition switch.
You need to know if the alt is getting a signal and has batt voltage.

The Alternator is controlled by the voltage regulator, type is located inside the Powertrain control module, you guessed it the alternator is computer controlled. You will need the dealer to look into this before you waste anymore money on parts.

Having wiring problem where battery light stays on afterreplacing alternator

Check wiring in your. I also own a Chrysler and the electric map manual says that it can be the battery the alternator or the car's wiring. Check for faulty wires and fuses, also for a short circuit (those can make battery die in a short time depending on how intense they are)

earth cable from engine to chassis corroded or chaffed or just plain rotted away

have the alternator bench tested for faulty rectifier diode pack
it may be charging the correct voltage but it is AC voltage and not DC voltage
in which case the battery will die quickly
next to check is the voltage regulator
it has to be 4.5-14.8 volts DC and if it in the ECM unit , will require a new ECM to fix

if this is a diesel its a days job,DISCONNECT BATTERY UN DER PASSENGER SEAT take front grill and the front cross member off drain radiator loosen all bolts on radiator do not undo any connections on air con. jack up car remove plastic belly plate remove drivers side wheel and inner plastic arch cover ther is also a strut that needs to be removed,using a screwdiver prise off the fan timing belt then remove 4 bolts underneath that hold the radiator up you will then need to remove drivers side headlight to gain accsess to the bottom alternator bracket, with this done you can then carefully remove the alternator and remove the bush box and replace the bushes