Okay, I am a newbie here but let me try.

For people who have never worked for a living, any job may instill a valuable sense of self-worth and open doors to better jobs in the future
(A) may instill a valuable sense of self-worth and open doors to better jobs in the future - ok
(B) might instill for them a valuable sense of self- worth and to open doors to better jobs in the future - instil for them is wrong
(C) may, in them, instill a valuable sense of self-worth, opening their doors to better jobs in the future - again awkward construction... also opening their doors doesn't seem to be good.... i think opening doors to new jobs is correct.
(D) opening the door later for a better job and giving them a valuable sense of self-worth now - opening is incorrect as this doesn't complete the sentence
(E) may open the door for a better job later and giving them a valuable sense now of their self-worth - because of "and" the verbs open and give should be in same form for parallelism.