Guys, you're missing the point. Yes, they didn't know he had it, but you don't need to be consciously aware of the ring for it to affect you, right?
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But that's beside the point. If they knew he had it then, then they would have probably not helped them.
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Yes, but... When they denied the fellowship help with taking the ring to Mordor, could Gandalf not have taken the opportunity to point out that they had, unwittingly, already carried the ring with no ill effects?
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Possible. But did Gandalf know when exactly Bilbo got the ring?
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I don't think it's ever explicit, but an intellect such as his probably could have logically inferred it.
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Regardless of the Ring's power, or lack thereof, Mordor was still packed with orcs, the Nine Ringwraiths, and their fell-beasts. Not to mention the Eye of Sauron constantly watching over his lands.