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.
I'd also throw in a vote for the early-80s Minnesota North Stars. The team that made the Final in 1981 had a core that was incredibly young even by 80s standards. There were the two big junior scoring stars Bobby Smith (22) and Dino Ciccarelli (20). Steve Payne (22) had 17 goals in 19 games in those playoffs. Craig Hartsburg (21) and Tom McCarthy (20) were highly regarded young stars whose careers were off to impressive starts. Hometown hero Neal Broten (21) had just joined the team after the 1980 Olympics and a season at the University of Minnesota. Don Beaupre (19) was already considered one of the games best young goalies.
Plus, Lou Nanne had adopted the Sam Pollock model of acquiring high draft picks from weak teams. In '82 they grabbed the much-hyped Brian Bellows with the #2 overall pick, and in '83 they had the #1 choice overall (Brian Lawton).
With all that young talent you'd think they'd be set for the 80s, but the team wallowed in mediocrity for most of the decade.