I took mine apart and cleaned the laser lens with isopropyl alcohol and a cotton bud (USA English translation = cue tip). The problem persisted even though this method/trick worked for me previously. As a last ditch attempt, I took it apart and literally just blew air from my mouth around the circuitry (not recommended as small bits of saliva might cause a short circuit and a completely dead drive; I only did this as I have no compressed air and I was willing to throw it in the bin (trash) if it didn't work afterwards, especially as a new one is already being posted to me as I type). Amazingly, it worked.
N.b. Before blowing air, I also inserted a disc a few times into the drive without the metal cover on it, with it connected via external USB - SATA connector; without the cover on I had to help guide the disc on to the central disc spinner/retainer (sorry, don't know the technical term). This may or may not have helped eventually get the drive functioning properly again (perhaps it freed up one of the mechanisms??).
Anyway, I hope documentation of my experience might help someone else with a stubborn drive at some. point in the future. Mine is now working perfectly - it was DOA inside a 2nd hand MBP from eBay.