It's easier to understand if we rearrange the words... "It appeared from the very beginning to be a doomed prospect, and that was the source of these dilemmas". So let's invent an example. Lets say someone decides to build a boat out of paper. He's an eccentric fellow so this doesn't surprise his friends, but they explain to him that "this is a doomed prospect" and it couldn't possibly work. However, he isn't discouraged by their skepticism and he builds the paper boat anyway and offers to take his friends for a ride on the lake. Well of course, in the middle of the lake the boat disintegrates and turns into mush because it has soaked up so much water and the group finds themselves swimming in a cold lake far from the land. They are in a dilemma ! They think to themselves... "The source of this dilemma lies in what appeared from the very beginning to be a doomed prospect"

i think it would help if you included the rest of the sentence! but this is a very complicated way of saying something like: The problems are caused by a factor that (from the very beginning) made it seem that things weren't going to work out.