No she wasn't always a demigod nor stated to be...
Golden Age she was simply a member of a tribe of Amazon Women...
Silver Age she was was mortal but got her powers through blessings of the gods.
Bronze Age she was molded from clay...
Now in Modern Age she was molded from clay and given powers from different gods..
Various deities and concepts from Greek mythology were blended and
incorporated into Wonder Woman's stories and origin. Diana was formed
out of clay of the shores of Themyscira by Hippolyta, who wished for a
child; the clay figure was then brought to life by the Greek deities.
The Gods then blessed and granted her unique powers and abilities –
beauty from Aphrodite, strength from Demeter, wisdom from Athena,
speed and flight from Hermes, Eyes of the Hunter and unity with beasts
from Artemis and sisterhood with fire and the ability to discern the
truth from Hestia.
She eventually got killed and became a god...
The demon Neron engaged Diana in battle and managed to kill her.
The Olympian Gods granted Diana divinity and the role of the Goddess
of Truth who started to reside in Olympus; her mother Hippolyta then
assumed the role of Wonder Woman and wore her own different
incarnation of the costume.
In New 52 Zeus is her father so that does make her a demigod.
As well as your mention of Justice League Unlimited where Hades claims to be her father, although I can't find anywhere saying that he was telling the truth...
So overall Wonder Woman was never really a demigod until recently.