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But if the Vala is Morgoth, how does Mordor fit into the equation?
And no, it's not Angband or Utumno either.

Though I suppose that you could say that Morgoth was resposible for Sauron being the way he was...but Mordor still wouldn't correspond with the other clues. sweatdrop

Is it Numenor? It had multiple names, and it was through Souron's deception that it was destroyed, thus the end of an era. But Isildur took a seedling of the white tree and went to middle earth, thus the beginning of a new era.

Is it Arda?

Formed from a Vala's wrath: Melkor participated in the music of the Ainur which created Arda. He attempted to sing his own theme to become the master of this creation.

End of an era: The "era" would be the time before Arda was created.

The Birthplace of this Vala's hate: Eru ended the song and informed Melkor that his disruption is a part of the creation which Eru intended. Melkor, desiring control of Arda and ashamed by Eru's accusations, begins to hate the other Valar to whom Eru had given Arda.

Beginning of a new age: The "new age" being the first age.

This is why I believe it is Arda.

stare Uh...if Arda is not the answer perhaps you should tell us the answer or another hint.....

The answer eludes us...

No, Arda is not the answer.

Answer:-continues to elude you-
Me:-catches answer- Caught you!
Answer: gonk
Me: And the answer is...
Inland Sea of Helcar

When Morgoth destroyed the Two Lamps, Illiun and Ormal, he "cast down their pillars." The pillars were made of ice. Now, the pillar of Illiun was called Helcar, and when it was cast down it melted and formed the Sea of Helcar. Thus ended the Age of the Lamps.

One of the bays of the Sea of Helcar was Cuiviénen, which is where the elves first awoke. As is stated in the preface to The Silmarillion, which was written by Tokien, that "...the Elves...were peculiarly his [Morgoth's] enemies, and the special object of his desire and hate..." The awakening of the elves was the beginning of the Age of Stars.

The name of the Sea of Helcar was taken from the pillar of Illiun, and therefore is not its own name, but belonged to something else before.

Don't be so hard on yourself. It was hard and the clues were very vague... redface