hopeless

As adjectives the difference between hopeless and incapable

is that hopeless is without hope; despairing; not expecting anything positive while incapable is not capable (of doing something); unable.

As a noun incapable is

one who is morally or mentally weak or inefficient; an imbecile; a simpleton.

As adjectives the difference between abject and hopeless

is that abject is (obsolete) rejected; cast aside while hopeless is without hope; despairing; not expecting anything positive.

As a noun abject

is a person in the lowest and most despicable condition; a castaway; outcast .

As a verb abject

is (obsolete) to cast off or out; to reject .

As adjectives the difference between hopeless and despairful

is that hopeless is without hope; despairing; not expecting anything positive while despairful is characterised by despair; hopeless.