Thank you GoingHam. Everything there makes sense, but still hasn't solved my problem.
I ended up doing the USB thing, and the keyboard does switch on, and at first I managed to make LSDJ say "I80" (I guess that the keyboard was somehow synced), but it wasn't working. Then, all of a sudden, it stopped displaying I80 and so I'm stuck.
I checked with my multimeter and with the male PS/2 connector that the connections were fine and so it seems! The only weird thing is that when I probed the "data" and "clock" wires of the keyboard on my oscilloscope, they were both in "high" state, and only went for the logic "down" when pressing keys, but both of them! I thought the clock would have a steady periodic "pulse" or something, and the "data" aperiodic signals when pressing keys... It's all weird.
What manufacturer of keyboard/ model# are you using?
The vast majority of ps/2 keyboards (atleast that I've run into) aren't LSDJ compatible.