The correct synonym to convey a tone of hopelessness in place of "useless" is pointless.
Reason: "Pointless" suggests a lack of purpose or efficacy, which aligns well with the sense of hopelessness in the situation described. Both "useless" and "pointless" imply that the struggle is futile, but "pointless" carries a stronger connotation of despair and resignation. "Needless" implies something that is unnecessary, while "shameless" and "flawless" do not fit the context of hopelessness at all.