Let's go with the presumption made in "The City on the Edge of Forever" that Edith Keeler's pacifism led to the United States either not becoming involved in World War II, or becoming involved too late.
Under such a scenario, my suspicion would be that the Third Reich would have conquered the United Kingdom, Ireland, France, etc., and would have eventually come to dominate the Kingdom of Italy; Fascist Italy would become a client state of the Reich. I think that the Reich and the Soviet Union would have ended up going to war as they did in the real world, but that it would have ended up devastating but not destroying both sides, since the Germans would no longer have had their resources tied up fighting a war on two fronts. Eventually, they would have had to come to terms with one-another.
Meanwhile, the Japanese Empire would have had free reign in most of Southeast Asia and the Pacific. Australia would have been attacked, and either had some of its territory seized or have come to an agreement to become a Japanese client state. Japan would have turned its attention to the United States; an already-reduced (because of domestic pacifism) Pacific Fleet would presumably have been destroyed, and the Japanese may well have decided to target the West Coast (which was a constant fear of Americans at the time). This may or may not have eventually coincided with German attacks from the East Coast, possibly leading to a version of what was seen in ENT's "Storm Front" -- an East Coast occupied by the Nazis, a puppet government put in place in Washington, the populace subject to Nazi propaganda.
Whether or not the United States was ever completely conquered or the invasions repelled, I think this would have reduced the United States to a third-rate military power. It would not have been a major factor in international politics going ahead.
From there, then, we'd have three major empires vying for power -- the Third Reich, the Soviet Union, and the Empire of Japan. Eventually, this would have ignited into another major war.
I suspect that it is impossible to predict technological development in such a counterfactual history. Early space program successes may have been replicated, given the successes of the Soviet Union and of captured Nazi scientists who worked for the U.S. after the war. Atomic weapons would likely have been developed, if a few years later. I suspect that without the United States and United Kingdom, the miraculous advances in computing and telecommunications we've had in the last fifty years would have been severely delayed, or gone undeveloped. So, probably either no Internet and Web, or a much more primitive Internet and Web. Personal computers would likely be more primitive.
Add to this the significant loss of skilled and brilliant scientists, researchers, entrepreneurs, etc, as a result both of the wars, and of the subsequent genocidal campaigns brought about through a Nazi victory.
So I think it's probably fair to say that by 15 April 2063, Zefram Cochrane, even if he still exists, would not have had the infrastructure--not the economic infrastructure, not the educational infrastructure not the military infrastructure of a former major military power--available to him to either conceive of or build the Phoenix
. As such, there would have been no warp flight, and the T'Plana-Hath
would not have landed in Bozeman, Montana, to make First Contact.
Indeed, if Vulcan survey vessels were monitoring Earth during that timeframe, they would likely have concluded that a world dominated by three mass-murdering totalitarian states would be best avoided.
No First Contact in 2063? No United Earth. No United Earth, no Nathan Samuels and Jonathan Archer to push for a Coalition of Planets. Also no one to help the Syrannites overthrow V'Las, restore the original teachings of Surak, combat Vulcan imperialism, or uncover Romulan agents influencing the Vulcan government.
The recent novel DTI: Forgotten History
by Christopher L. Bennett features an alternate timeline in which Earth does not become a player on the interstellar scene in the 22nd Century. By the 23rd Century, Vulcan has become a militant, imperialistic state that has conquered the Romulans, while the Andorians and Klingons have united in opposition to Vulcan. The quadrant is ravaged by war.
So, yeah, without Earth to serve as the "honest broker" who brings Vulcan, Andor, and Tellar together--who helps Vulcan return to its roots and end its neo-imperialist government; who mediates conflicts between Vulcan and Andor and between Andor and Tellar; who prevents wars of aggression based on false intelligence; who pushes for a Coalition of Planets; who uncovers Romulan manipulations and then fights a war against Romulus--it seems fairly clear that there's no Federation.