In "Where No One Has Gone Before" (TNG), Picard referred to his mother in the past tense, implying she was no longer alive in 2364. This is reinforced by "Family" (TNG), in which Picard returned to his family home in France, no longer occupied by his parents. In "Night Terrors" (TNG), Picard recalls that as a young man, he saw his "grandfather deteriorate . . . from a powerful, robust figure . . . to a frail wisp of a man, who couldn't even remember how to make his way home." Picard once recalled (in "Conspiracy" [TNG]) that his "oldest and closest friends were Jack Crusher, may he rest in peace, and Walker Keel." Keel was later killed when the alien parasites blew up the Starship Horatio in that episode.
In "Rascals" (TN G), Picard noted that he'd spent 30 years of his life on starships, although he took command of the Stargazer some 36 years prior to that point. (He clearly had at least a few years of starship duty prior to that point, as well.) Picard may simply have been rounding oft the number, but it seems possible that there was a period of at least six years after the Stargazer disaster during which he was not aboard a starship.
2305: Born in LaBarre, France on Earth ("The First Duty" [TNG]).
2322: Applies to Starfleet Academy, but is rejected ("Coming of Age" [TNG]).
2323: Admitted to Starfleet Academy ("Coming of Age" [TNG]).
2327: Graduates Starfleet Academy ("The First Duty" [TNG]).
2333: Assumes command of U.S.S. Stargazer ("Tapestry" [TNG]).
2355: Stargazer nearly destroyed at Maxia Zeta ("The Battle" [TNG]).
2364: Assumes command of Enterprise-D ("All Good Things [TNG]).
2266: Captured by the Borg ("Best of Both Worlds, Parts I and II" [TNG]).
2371: Enterprise - D destroyed (Star Trek Generations).
2372: Assigned to command Starship Enterprise - E (Star Trek: First Contact).