Super question. I think the way to go about figuring it out is not trying to remember the year or team, but approaching from the players. That said, more recent teams (Marlins, Devil Rays) can be scratched off the list.
It's hard to even think of cases of bad teams that had even three HOF players. Initially, I kept trying to piece it through with Phil Niekro, Sutton, Ryan, or Winfield, because they played so long and on so many teams. I was stuck on the Orioles for a while. Murrey and Ripkin played together, but I couldn;t place them on a team losing 100. Besides, who else played with them? Was Palmer still around then - I just can't remember anymore.
Then, I tried to see if I could Place Mays or McCovey on a losing team and again, no cigar. Brock? Nope. Schmidt and Carlton? Nope. Bench? No. Stargell and Clemente maybe? No dice. Ernie Banks....
Hmm, the Cubs are perrenial losers (that is, they lost a lot). Banks was a great player. Who else did the Cubbies have in those days? Well, I'm pretty sure that Billie Williams is in the HOF and he played a long time with Banks, so that's two. Now, I remember that Ferguson Jenkins won 30 games in the early seventies with the Cubs, but the question is: Was he around in those early days? I'm going to assume yes, since that would make three.
My problem is that I am stuck on 3 and can't think of a 4th. I also don;t have a clue as to what year it would have been. Leo Durocher was probably the coach, I know he coached them for several years in the late 60's (especially '69 when he lost to the Mets). My guess is that it would have been his first year with the team, I just don't remember when that was. Incidentally, he was a hall of famer himself, but I assume you're looking for another player.
So that is where I am stuck. Help would be appreciated. I love these types of questions!