The Sin of Elves

[Maédhros]

The Valar went to war against Morgoth to protect the Elves. Why, then, did they only have an indirect influence on the War of the Ring? Did they like Elves better, and since they were leaving, did not care of the fate of everyone else?

A very interesting question, which i have wonder myself. I think that you could say that they could have liked elves better because they could interact with them in Aman, but couldn't with men.
If you see it from a different perspective, you might say that the Valar waged war against Morgoth because of the coming of the elves, as you have stated, and when men arrived in ME, the Valar didn't do didly squat for them.
It leaves me wonder why.