You said that at one point you could review the structure of the DVD (the audio and video directories, and the VOBs). If that's right, you're close: a DVD is just those files and can be played if the files can be read. Can you try launching DVD Player directly yourself, from Spotlight? How about your CD & DVD preferences--how are those set, in System Preferences? (They appear only when a DVD drive is connected.) What about information that appears in "Disc Burning" in System Information (Spotlight again, or Option-click "About This Mac" on the Apple menu)--does that indicate that your drive is connected?
Of course, it could be anything--optical media is famously finicky--but it does sound to me like a simple configuration problem. I can't think of any obvious incompatibility on the hardware side, although I suppose you could try plugging the "Superdrive" into a powered hub to try and rule out a power issue that is somehow unique to modern Macs. If you've been using this for years, you're really limited to testing whether it reads other discs, but if you're not interested in buying more hardware, I really can't suggest anything else.
Good luck.