I have the ambition to write a semi-parodic TL on this theme, perhaps titled 'No Good Deed Goes Unpunished' or perhaps 'War: A Comedy', but I doubt I'll get around to it. Salient features would be:
1. The Sarajevo assassins miss completely (possibly shoot each other by mistake). July 1914 Crisis averted.
2. Civil War breaks out in Ireland by the end of 1914, straining not so much London's resources as her relationships. The situation is under control by 1916, but the diplomatic fallout encourages the CP to believe Britain will not/ cannot intervene in a Continental conflict. A Conservative government replaces the Liberals, who have torn themselves apart (again) over the Irish Question. The sale of the Dreadnoughts to Turkey goes ahead as planned. The French Army gets rid of its red trousers and extends its conscription period. Russia double-tracks a lot more of its railway lines by the end of 1916.
3. Franz Ferdinand becomes Emperor in 1916 (FJ dies as OTL). He begins an ambitious project of political restructuring in A-H, perhaps announced in a Christmas Message to His Faithful Peoples.
4. His Faithful Peoples respond enthusiastically. By summer 1917 A-H is ungovernable as restructuring gets a little out of hand. (Some may recall that the Russian for restructuring is perestroika.)
5. Italy, Serbia and Romania start rubbing their hands and choosing tasty-looking morsels of territory. Sometime in August 1917, one of them goes too far and it's on like Donkey Kong. Germany feels forced to mobilise in support of A-H, but with great foreboding; France and Russia have improved their armies considerably in the last 2-3 years.
6. Russia mobilises in support of its Balkan allies, France follows suit. London makes it very, very clear to Berlin that Belgium is off-limits. Berlin decides that fighting Russia and France at the same time, with A-H effectively out of the game (at least for the time being), is quite enough to take on without risking British intervention; so they stand on the defensive in the West and launch their main offensive in Poland. French offensives in Alsace make little progress.
7. The Balkan states amuse themselves carving up A-H. London gets nervous about Sofia and Athens and asks for assurances that they will not backstab Serbia. They provide the assurances. London then becomes nervous about Istanbul's attitude and asks for assurances that Turkey will not backstab the Balkan states; the Young Turk regime declares itself committed to peace.
8. Turkey backstabs the Balkan states.
9. By Christmas 1917, the Germans have overrun Russian Poland, forcing a Russian withdrawal from Galicia (and creating a power vacuum there), but A-H has fallen apart decisively, with FF being derisively nicknamed 'the Mayor of Vienna'. Hungary declares independence, and celebrates this by fighting Serbia and Romania. Italy seizes Dalmatia; the Croats demand that Budapest resists this, but the new Hungarian regime is too busy already; the Croats therefore declare independence from Hungary. The Czechs declare independence, but are invaded by the Germans. The British press, never known for its commitment to logic in foreign affairs, decides that this is Unacceptable, and that Something Must Be Done.
10. Britain intervenes in early 1918. A British operation at Gallipoli goes badly, with several RN battleships lost to a combination of mines and the (British-built) Turkish battleships. A French landing at Alexandretta goes much better, severing Istanbul's connections to the Middle East.
11. During 1918 Berlin realises that the situation is unlikely to improve. Germany still holds Alsace-Lorraine, but Britain has now joined the war so the balance of forces in the West has turned against them. Berlin has gained Bohemia and Poland, but Vienna is no longer a viable ally. By the end of 1918 Berlin is putting out peace feelers. France - which has not been invaded, but has lost a lot of men for little gain in territory - is receptive.
12. The peace deal of 1919 infuriates St. Petersburg but is actually (compared to OTL) massively to its advantage. It restores the status quo ante in the West and pacifies Britain and France with vast chunks of the Middle East, taken from Turkey. Germany annexes the German-speaking parts of Bohemia. Russian Poland and Galicia form a new independent Poland as a client state of Berlin (thus providing a buffer against Russia). Hungary gains its independence; the rest of the Balkans remains too confusing to describe briefly. Russia has therefore lost Poland, but avoids the Revolution and gains time to develop. The reverses of the war weaken the Tsarist regime and create the political space for a more liberal regime to succeed and get the credit for the economic boom of the 1920s.
The TL would end with a distant postscript describing the flight of Soyuz 1, in which Sergei Komarov survives; because in this ATL Russia there are at least a few happy endings.