The Silmarils

[Gwaihir the Windlord]

no, i think Melkor was unable to overthrow the Noldor completely because he did not have the power to do so.

Mans has said it. Morgoth did overthrow the Noldor. It took hundreds of years, but in the end they were utterly crippled and merely awaiting annihilation in Morgoth's own time, while Beleriand was wholly under the control of his forces.

In the end, he was defeated -- but by Valinor. He crushed the Noldor. Perhaps a fairly good analogy could be found in the example of WWII France.

As for the initial question, Voralphion is correct. The Silmarils were indestructible in Arda;
So that no violence in Arda may mar or break them.
Feanor, their maker and the only one who knew their secret, was the only one who could have destroyed them -- as Yavanna asked him to do after the death of the Trees.