Car: Buick Park Avenue 2003 (Standard) - 180k Miles - Automatic

Hello! I was driving my car to work when all of a sudden my wheel locked up, pressing the gas did nothing, and the car stalled out so I pulled over. I waited a while, tried to start the car again, but when turning the key in the ignition, not even a click happened, but the lights and AC and such would come on. I scanned with my OBDII and the code "1639" appeared and upon research I found the PCM has a failure. 

Now here's my question: I took out the PCM and looked at the information on the sticker and it suggests that it's not the original and when searching up the HDW numbers (HDW 12202610, SERV 12209624), I get that it's for a 2001~2002 Buick Le Sabre. Is that compatible with this Buick Park Avenue 03? I have not found anything that seems to suggest so. Is this potentially related to it's failure? 

Admittedly, I do not know much about cars. If anyone can confirm that what I had inside my car was compatible, I'd be glad. This car was passed down to me from my father who has no recollection of ever changing the PCM since he bought this car brand new back then over two decades ago.