What If the Doctor Never Met Donna Noble?

(Spoilers for Turn Left and the whole of Series 4 ahead.)It's a Doctor Who/What If crossover!

Turn Left
Based on: The Runaway Bride
The true history: Donna goes to work at H.C. Clements, meets Lance who fills her up with particles that whisk her off to the TARDIS. Enter the Doctor who goes on to destroy the Racnoss responsible. It's all Time Lord hell and fury until Donna wakes him up and makes him realize he's going too far. They escape, and though he doesn't travel with her for another year yet, he continues to save the world in the company of pretty girls.
Turning point: What if Donna never went to work at H.C. Clements?
Story type: Everybody dies.
Watcher's mood: Dusty Rose.
Altered history: Since Donna takes a job at a photocopy place instead, she never boards the TARDIS, so another person - perhaps Lance himself - is impregnated with the particles. The Doctor catches wind of the plot and, like in the original history, floods the Racnoss chamber. But without Donna there to snap him out of it, he drowns without a chance to regenerate. The Doctor is dead. When the Judoon take the hospital to the moon, Sarah Jane Smith and the kids take his place (indicating that Mr. Smith must screen events and not send Sarah where she's not really needed). They die stopping the plasmavore.
As does Martha who gives her last oxygen to fellow student Oliver. Because the Doctor never goes to the year 1 billion, he never awakens the Master, so Lazarus' experiments never amount to anything, and Harold Saxon never becomes Prime Minister. The next Christmas, however, he's not aboard the Titanic to prevent it from crashing and London is destroyed.
Originally, one supposes that Donna would die there, but she and her family are saved by the interference of Rose Tyler (although it's quite possible Donna would have used the raffle ticket anyway... if indeed Rose didn't rig the contest). The whole of Southern England is flooded with radiation, 7 milion people in need of relocation, and Donna and her family are sent to Leeds to live with many other families in the same home. The USA might have helped the UK except that 60 million people have turned into Adipose.
Seems like America would have been a better target in the first place, eh? North America is famously fat and Doctorless. Then comes the ATMOS crisis. Britain is largely spared because it doesn't have a lot of petrol anymore, but the rest of the world is choked by the fumes. This time, it's up to Torchwood to stop the Sontarans.
They succeed, but Gwen and Ianto are killed, and Captain Jack, unable to die, is transported to the Sontaran homeworld. Affairs in Britain get worse and worse - labor/death camps for immigrants, and so on - and then the stars start going out. How exactly Davros initiates his plan without stealing Earth isn't made known, though since the Medusa Cascade is a transdimensional anomaly that allows his reality bomb to affect all universes, he might have stolen a different Earth (the Cascade's properties may also be the reason why we can see the stars going out despite the fact that at light-speeds, we would never notice). This is Donna's push-comes-to-shove moment, and from there, she accepts Rose's offer to erase this alternate history.
Series canceled as a result: Doctor Who, Sarah Jane Adventures and Torchwood. In that order.
Untold and unexplained: In order... How were the Carrionites defeated? Maybe Shakespeare is as brilliant as the Doctor said. What about the Daleks in Manhattan? They might have split into factions and killed each other in an underground civil war. Cahn would still have left to save Davros from the Time War. The people of New Earth would never have been rescued from terminal gridlock. The ship in 42 would have been destroyed by the star. The Family of Blood would still be at large (and lots of people in 1913 would still be alive). Humanity never reached Utopia. How were the Pyroviles defeated? That one's harder to figure out, but as the Doctor has often BEEN to Pompeii in non-canon stories (including a passing reference to it in the New Series Novels), there are plenty of Doctors on hand to stop them (they were just always occupied with other matters). If not, there's always a younger Captain Jack, who might have gotten involved during one of his cons. The war with the Hath is still going on (and Jenny was never created). Agatha Christie figured out the case of the Unicorn and the Wasp by herself. The Library is still empty (there is no River Song either, not as we know her). And the creature from Midnight is probably on the loose. As for the other dead heroes, the absence of Tosh and Owen means we're after Series 2, and if Clyde was already part of Sarah's team, the events of her first series may well all take place before Smith and Jones.

Things to watch out for
Donna's Destiny: There are two things to consider here. First, there's Rose's prophecy - "You're gonna die." In combination with other clues (your song must end, River's reaction), it does a good job of making you believe Donna will pay the ultimate price. However, for all her omniscience, Rose definitely doesn't know her own future, including the events of Journey's End. So she really is talking about that meeting with the truck. Second, there's Donna's importance to reality. However they manage to calculate the time lines, she's as much a focal point as the Doctor is. Time actually bends around her. That's because being the Doctor Donna (or any Time Lord) actually ripples forwards and backwards in time. The universe is driven to create the Doctor Donna because the Doctor Donna has existed in some potential the Time Beetle has here erased. The Doctor remarks on the coincidences surrounding Donna, like his meeting her twice, etc. In this story, was it a foregone conclusion that she would win the raffle and survive? That Rose would be pulled from her dimension to help?
Wibbly-wobbly, timey-wimey: Read the above if you didn't quite get your head around it the first time. The Doctor Donna creates herself. What's the other character that created itself? Bad Wolf, which also appears here.
How? Since Rose became time and space back in The Parting of the Ways, she had access to these events and their disruption. Just like she left all those other messages in Series 1, she left this signal here as well, at the Chinatown planet, to alert the Doctor.
They call it foreshadowing: The stars going out leads pretty directly into the next episode. The Doctor's death foreshadows his death in that episode, but Donna's death/not death also mirrors his aborted regeneration.
Are you my mummy?: There is no actual parthenogenesis in this story, but the idea that there are two Donnas existing simultaneously is reflected in the two Doctors of the next story.
Back problems: This is the payoff to the prophecy in The Fires of Pompeii. Again, we have a temporal being that echoes back into the past.
The bees' knees: Donna's mum mentions that you don't see bumblebees anymore.
Dusty Rose: So Rose returns by dimensional cannon, but that return asks more questions than it answers. How is she moving about in time as well as dimension? And how did she pull off those tricks where she called out to the Doctor in earlier episodes (Midnight especially)? We could surmise that the transdimensional technology her version of Torchwood is using has temporal properties. Certainly she can analyze the time lines and other universes (enough to know they're all in danger). So perhaps they only had enough power to send transmissions, and if Donna leaves a bend in spacetime, the Doctor surely must. Home in on that. By Turn Left, Rose loses access to her home dimension, which has collapsed and become Donna's alternate reality. She uses the technology to follow Donna's movements, help her out, and make contact with UNIT. If she's always wearing the same clothes, it may be just a one-day mission for her. Note that she is NOT using the TARDIS-powered UNIT time machine, and untested machine that requires a harness of some kind.
The reference section: Lt. Harris, the UNIT trooper at the scene, was one of the hypnotized goons in The Sontaran Stratagem, and Captain Erisa Magambo will appear in standard continuity in Planet of the Dead. The army isn't any smarter than UNIT, also shooting at car exhausts.
The Time Beetle is a member of the Trickster's Brigade, and the Trickster was the time-twisting villain in Whatever Happened to Sarah Jane?, another Turn Left-type story. On the UNIT time machine, mirrors are used to bounce the chronon energy. Finally, an explanation for the strange mirror-based Victorian time machine in The Evil of the Daleks!
And the Cloister Bell sounds, indicating the universe's impending catastrophic failure. It first rang in Logopolis, and most recently in Time Crash.

Next time: The cliffhanger to end all cliffhangers