In the future please do not plug PS/2 keyboards in with the PC on. There is actually a chance it can destroy hardware. Granted it is a smaller chance now that years ago, but still a real possibility.
Well, thanks for letting me know, I'll definitely never do that again.
Back to my little "issue", I did try to plug the keyboard using the PS/2 interface while the machine was off and it didn't "solve" the problem, same behavior. But I did find the solution/explanation.
I'm actually using a Dell laptop with a docking station and after doing some research, I discovered that there is an option in the BIOS called "Fn Key Emulation" which allows you to match the <Scroll Lock> key feature of PS-2 keyboard with the <Fn> key feature in an internal keyboard. And this option is enabled by default.
So, by default, on the PS/2 interface, the Scroll Lock key acted as a modifier and no scancode was sent when pressing it (at least that's my understanding), as I observed.
After disabling the option in the BIOS, the Scroll Lock key just acts "normally" on the PS/2 interface, it sends the expected scancode and the led turns on/off. The keyboard and the PS/2 adaptor are working just fine.