I'm working from memory on this, but considering that I just kicked this off a couple of days ago, it should be pretty close to what should be happening.
After completing the "Horn of Jurgen Windcaller" quest and receiving the greeting of the Graybeards, Arngier should have a dialogue option that says something to the effect of "I want to learn more about the Voice" or somesuch. Following up on that thread leads to the Words of Power missions.
As far as I know, there are only a handful of conditions where Arngier will not point you to Words of Power.
- If you have found all of the available Word Walls (apparently not the case)
- If you have killed Paarthunax (apparently not the case)
- (Maybe) if you weren't properly deferential to him during the "Way of the Voice" quest, but I doubt it
I've run into a couple of instances where he would not cough up a location because I already had a "Letter from a Friend" pointing me to the location of the Word Wall he was going to give me.
But I'm getting the impression from the OP's initial post that the option to ask about Word Walls isn't there at all rather than getting the "all is silent" kind of reply to the question. If that is the case, I'd look at whether the "Way of the Voice" quest terminated properly (the final state should be 160 according to the UESP wiki). I'm doubtful of that since the "Horn of Jurgen Windcaller" quest apparently finished (you did get the Horn from Delphine and take it back to Arngier, right?). If the Horn quest terminated properly, its state should be 60 and you should have the final piece of "Unrelenting Force". If all of those conditions are true, I'm well and truly stumped.
EDIT: The OP said that Paarthunax was alive and well -- that's a different quest that cannot happen until Delphine and Esbern are at Sky Haven, I think. Is it possible that the Words of Power dialogue options disappear at that point if they haven't been used? I'm doubtful on that point, but it's a possibility.