Using something called a CH341a Programmer, I was able to successfully repair the laptop.
This involved locating the BIOS Chip, figuring out what model it is, backing up the original BIOS Firmware (a .bin file), and finally, flashing the new BIOS Firmware with the appropriate serial information added.
Thankfully, HP Makes it easy to get the BIOS Firmware Image -- you just run the HP BIOS Updater tool and select the option that says "Copy BIOS Image to any file location (Advanced Users)".
Here's a great resource to help find out what your Board ID is so you can flash the appropriate BIOS Image:
[link|https://github.com/ISpillMyDrink/UEFI-Repair-Guide/wiki/HP-System-BIOS-Update-Utility|https://github.com/ISpillMyDrink/UEFI-Repair-Guide/wiki/HP-System-BIOS-Update-Utility|new_window=true]
One thing to note is that adding the serial information is a difficult task once the chip is flashed -- hence you should backup the original BIOS Firmware so you can extract the serial information and add it to the new BIOS Image before flashing it to the BIOS Chip.
To add the serial information to the new .bin file, you can either use a hex editor or you can use UEFITool. I just went ahead and used HxD, a hex editor, and copied over the serial information (which in my case was the data from hex address ``00000000`` to ``0002a000``) to the new BIOS image. Your hex addresses may be different, and in that case, you can request help from members of servers that specialize in these types of repairs for more help as to how to properly extract serial information.
This is very much a last-ditch DIY repair, so I strongly suggest you remain cautious throughout the entire process; any mistakes you make have the potential to permanently damage your system.
With that said, a great place to start would be with this video:
[link|https://www.youtube.com/watch?v=FJ0rAM-N7tY|https://www.youtube.com/watch?v=FJ0rAM-N7tY|new_window=true]
The owner of that YouTube video also runs a Discord server where you can get more knowledge on how to do this procedure correctly. I was graciously assisted by some of the server's members, and that's pretty much how I, a complete beginner, was able to get this arduous process done.
It's difficult for a beginner, no doubt, but it can be done with a lot of effort.