I'd like to nominate a couple of versions of the Buffalo Sabres:
The mid-70s: The future looked bright for the Sabres after the 74-75 season. They finished tied for 1st overall and made it to the Stanley Cup Final, but the core of the team was very young. Only one skater (Fred Stanfield) was over 28; Perreault was 24, Martin and Ramsay 23, McNab 22, Gare 20. Their oldest defenceman was Jerry Korab at 26; the rest of their blueliners were 23 or under and looked very promising (Schoenfeld, Hajt, Fogolin, etc.). The only area of the team that seemed in decline was goaltending, but in the 1975 draft they took the two goalies who ended up having the best NHL careers (Edwards and Sauve).
Yet despite it all, in the four seasons from 75-76 to 78-79 they never won a single best-of-seven series.
The early 80s: This was the Scotty Bowman era and by 1983 he had traded veterans for multiple first round picks and young prospects. They had a good playoff run in '83, and lots of young talented players with promising futures: By my count they had 9 former first-rounders 25 or under playing regularly on their roster that year; most notably Housely (18), Andreychuk (19), Ramsey (22) and Foligno (24). Then they had 3 of the top 11 picks in that years draft (Barrasso, Lacombe and Creighton).
But it would be a full decade before they ever won another playoff series.