I too was a Celtic fan growing up, starting with the teams with Cowens, Havlicek and White. The team that you mentioned with Bird, McHale, Parrish et al. was amazing.
There are probably many reasons for their present state, but it seems that in the NBA once you become mediocre, it's not easy to improve. They showed some signs of improvement at times, but haven't been able to play well consistently. I don't think Danny Ainge has put them on the right track.
Anyway, the worst thing to have happened to them was the 1986 death of Len Bias, whom they drafted with (I believe)the second overall pick of the draft soon after winning the NBA championship against Houston. With Bias, I feel the Celtics would have won additional titles-hewas that good.
Secondly, the death of Reggie Lewis in 1993 (I think) hurt the team.
But these aren't excuses for their present poor play.