Question: After the passing of Denethor, Gandalf says the following:

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> Though the Stewards deemed that it was a secret kept only by themselves, long ago I guessed that here in the White Tower, one at least of the Seven Seeing Stones was preserved. In the days of his wisdom Denethor did not presume to use it, nor to challenge Sauron, knowing the limits of his own strength. But his wisdom failed; and I fear that as the peril of his realm grew he looked into the Stone and was deceived: far too often, I guess, since Boromir departed.
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This seems to be just well informed speculation by Gandalf but I am wondering if perhaps there was some critical event that was a key factor in Denethor starting to use the Palantir? I cannot find anything referring to it in the LOTR appendices - is anything regarding this matter mentioned elsewhere?

Answer: 
Well, we have an obvious upper bound of TA 2988 (from Appendices A & B):

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> 2988 Finduilas dies young.
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> ‘After [Finduilas'] death Denethor became more grim and silent than before, and would sit long alone in his tower deep in thought, foreseeing that the assault of Mordor would come in his time. It was afterwards believed that needing knowledge, but being proud, and trusting in his own strength of will, he dared to look in the palantír of the White Tower.
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We have a lower bound, also from Appendix A, of "before his sons grew to manhood":

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> ‘In this way Denethor gained his great knowledge of things that passed in his realm, and far beyond his borders, at which men marvelled; but he bought the knowledge dearly, being aged before his time by his contest with the will of Sauron. Thus pride increased in Denethor together with despair, until he saw in all the deeds of that time only a single combat between the Lord of the White Tower and the Lord of the Barad-dûr, and mistrusted all others who resisted Sauron, unless they served himself alone.
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> **‘So time drew on to the War of the Ring, and the sons of Denethor grew to manhood.**
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His sons were born TA 2978 and 2983, so it's likely that his first viewing through the palantir took place between TA 2988 and 2998. The reason I give them 20 years for manhood is because that's when Aragorn was adjudged to have entered his manhood as a slower aging Dunedain by Elrond:

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> 'when Estel was only twenty years of age, ... Elrond looked at him and was pleased, for he saw that he was fair and noble and was early come to manhood.
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So that ten year gap is the most likely case for when he started using it, triggered by the death of his wife. Interestingly, that actually puts him earlier than Saruman and his entrapment:

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> c. 3000 Saruman dares to use the palantír of Orthanc, but becomes ensnared by Sauron, who has the
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More is said in Unfinished Tales concerning this matter.

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> ...when and why Denethor had dared to use the Stone was and remains a matter of conjecture.
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> His 'grimness' was first observable to others after his wife Finduilas died in 2988, but it seems fairly plain that he had at once turned to the Stone as soon as he came to power, having long studied the matter of the palantiri and the traditions regarding them and their use...
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From The Palantiri, UT

If this is true, then he started using the palantir in 2984 when he succeeded his father.