I vs E: First of all, Trent is definitely NOT an E. Most certainly an I.
"In contrast to his on stage personality, Reznor is often credited to be shy, soft spoken and a bit of a recluse."
"Trent Reznor struggled with depression, social anxiety disorder, and the death of his grandmother (who raised him)."
Sounds like an introvert to me. An extrovert suffering from social anxiety? Sounds like an oxymoron.
N vs. S: Secondly, definitely N over S. His music has always been fairly innovative (at least it was in the 90s) and unique. He also claims David Bowie's "Low" is his favourite album. Anyone familiar with that album knows it's definitely one of Bowie's weirder albums. Seems like an N taste.
"Reznor is a fan of David Bowie, and has cited Bowie's 1977 album Low as one of his favorite albums. Reznor has stated that he played the album constantly during the recording of The Downward Spiral for inspiration."
T vs F: In my opinion T over F. I think writing ANY lyrics requires digging into your F side so I can't see how quoting lyrics that show emotions proves he is an F (Ts have feelings too). When I listen to NIN the feelings I hear are very raw, almost childlike, which to me sounds like the repressed, underdeveloped feelings of a T. I would think a natural F would be much more eloquent at expressing their emotions. The feelings would be much deeper. Just think of "Starf**kers, Inc.". It was basically directed at Marilyn Manson. It's a great song but in reality is quite petty... childish even----> underdeveloped F side -----> Trent=T
P vs J: On this one I am really not sure. Trent apparently has amazing work ethic and is quite the perfectionist. Seems like a J trait. Doesn't sound like the open-ended laziness characteristic of a P (no offence Ps). Then again, INTPs CAN become obsessive in certain areas. Not sure on this one.
*All the quotes are from the "Trent Reznor" wikipedia entry.
For the record, I've (admittedly) watched a lot of interviews with the man, and I'd say the above one is easily one of the most relaxed and 'honest' that I've seen. Personally, I go with INTJ, but since we'll never know and his type doesn't really matter in terms of my continued enjoyment of his music, I don't dwell on the answer too much.