Assuming that we achieve immortality in our current state I would assume this means a cure for natural death. e.g no more death from old age. That still leaves death from murder, accidents, etc.

Given that reality, I still don't see the second part as solvable. Because at the root of it, what we would have to solve is man's inhumanity to man (greed, envy, hate). Because the reality is people you know and love are still going to die, maybe they live longer but there is still going to be death. At a certain point when you lose enough people it makes one tired in the soul. I am of the opinion that you have to eliminate all suffering for an eternal existence to be worth living and we as humans have been pondering that subject probably longer than any other human problem that has existed.

Now if we are talking about another form of reality say a simulation where none of that stuff ever exist and we upload our minds into it we are really no longer talking about eternal life in this existence. Rather we are talking about heaven, enlightenment whatever we want to call it just by a different name and the reality is, even though it may be a instantaneous upload, we still have to die to get there. If not we just exist in two realities one where we are immortal and a wholly different being and one we are still very mortal and still suffer from the imperfections of this existence.

I just don't see how it is solvable by making what we are now, live forever.