I am not 100 % sure if you are asking how to tell the PMD 661 original from the MKII or MKIII, but if that is part of the question, it is easy because the MKII is clearly labeled (I was going to say "marked", but that might be confusing
) MarkII, and the MKIII is totally different looking, more like a giant PMD 620.
MKII is labeled just above the LED's:
As for not recording, that is trickier. I think I recall an instance where someone tried the firmware upgrade from a MKII on their MKI, and it ruined the deck, but I may be wrong here. It seems odd that it would not record, but I'd check all of my presets or try creating new presets. Have you tried recording with the 1/8 input to see if that works? Different cables or mics? possibly set as Line in vs Mic in? Have you tried line in with a non mic source like a cd or cassette player? Phantom on for sure? Have you tried digital in if you have the capability?
In the presets, it is very possible to have the attenuation set so that the dB level is not hot enough to get a signal registering. I'd play with that and see if anything happens too. I'd be more specific, but part of the problem with set and forget presets is that I set and forget...