One more question: In terms of heat dispersing, it is better to position the system horizontally or vertically? Or does it not matter?
Since the system was pretty gunky, I figured it was likely some dirt or something that was preventing the disc drive from closing, so I took a cotton swap dipped in surgical spirit and stabbed it into the slot, scrubbing anything I could reach. This got the drive to close! But then... it had the opposite problem, and wouldn't open up, now stuck closed. I tried to pry it open and have probably bent the front of the drive a bit, but it wouldn't pop out. Eventually, I slammed my fist onto the top of the system as it was trying to open, and in a Fonz sort of moment, this worked to get it to open back up!
Deciding maybe I should stop fumbling around on my own with this thing, I looked up some information and guides. After seeing what the inside looked like and how the mechanism worked, I noticed that two of the gears and a belt could be reached without opening up the system. So I concentrated on cleaning those with a surgical spirit-dipped cotton swab. Once waiting to make sure it was dry, I closed the drive, and so far it seems to be back to working properly! Though, at some point a small piece of metal and a couple screws fell out of the drive, so I hope that isn't an important piece...
Finally, after twelve long years, I can at last play the Burger King games!