[Boromir88]

Do you believe that Denethor had no knowledge of a Hobbit possessing the Ring before sending Boromir to Rivendell?~Mansun

I do.

For the simple fact that even if Denethor knew Frodo possessed the Ring (which I don't think there's anything to suggest that he did know), Boromir sets out for Rivendell on July 4th 3018, Frodo doesn't leave Bag End until September 23rd and has no idea he's going to Rivendell until he runs into Aragorn at Bree on the 29th.

And as WCH mentions, most in Gondor seemed to think Isildur's Bane referred to the orc arrow that slew him. Faramir thought so until he deducted that Isildur's Bane couldn't have been an orc arrow:

'...Nor when the riddling words of our dream were debated among us, did I think of Isildur's Bane as being this same thing. For Isildur was ambushed and slain by orc-arrows, according to the only legend that we knew, and Mithrandir had never told me more.'~The Window on the West

Both Boromir and Faramir had a riddle in their dreams regarding Isildur's Bane...and as both would say they had no clue it was a Ring. Apparently neither did Denethor:

'Of these words we could understand little, and we spoke to our father, Denethor, Lord of Minas Tirith, wise in the lore of Gondor. This only would he say, that Imladris was of old the name among the Elves of a far northern dale, where Elrond the Halfelven dwelt, greatest of Lore-masters....'~The Council of Elrond

Even if Denethor knew Isildur's Bane meant Sauron's Ring, before Boromir left for Rivendell (which there is nothing suggesting that he did), he didn't let Boromir or Faramir know this bit of info. As both Boromir and Faramir's story say the same thing when they went to their father to interpret the Riddle...they both (at that time) thought Isildur's Bane were the orc-arrows that slew him.