Changing the past is impossible.
Time Travel.
The time-theory at work in the first two Terminator films is the very antithesis of the "No Fate" credo. And I'm quite certain that James Cameron was being intentionally ironic in leading his characters to believe that they could avert their fates.
T1 and T2 both operate as a causality loop brought about by a predestination paradox.
I'm not going to attempt to reconcile the events of T3 with The Terminator and T2 because T3 breaks the series' internal logic and time loop theory as laid down by James Cameron with the simple fact that it has moved Judgement Day. That isn't possible in James Cameron's Terminator films as the past cannot be altered only caused.
I'll explain why.
The great irony of the first two films is that as much as the characters would like to believe that "the future is not set" they are wrong.
Cameron's causal loop begins in T1 with the arrival of Terminator and Kyle Reese. Looking at the timeline from a linear and objective standpoint things progress as normal until 1984 when suddenly two travellers, or chrononauts, from 2029 show up.
There was no 'original' and alternate timeline where someone other than Kyle Reese was John's father. There is only the one timeline, the one they're in, and when that timeline hit 1984, these two chrononauts simply show up having been displaced from 2029. The events of the first film take place and Sarah Connor is impregnated, Kyle is killed and the Terminator is destroyed. Then the microprocessor chassis is recovered from the Cyberdyne factory floor and the research into neural-net computers begins, Cyberdyne builds an empire and secures defense contracts including the SkyNet program for SACNORAD. Meanwhile Sarah goes into hiding and gives birth to John who will grow up to one day lead the human resistance to victory against the machines.
The damaged T-800 chip left at the Cyberdyne factory was always the genesis for neural-net processors. Kyle Reese was always John Connor's father and Judgement Day was always August 29th 1997.
Time travel in this universe cannot change the past it can only cause it. Travellers to the past become the cause for events whose effects have always been.
In the T2 Extreme DVD Cameron states that this concept of effect coming before cause, a popular conception of time travel in metaphysical circles, was his intention with both films. The causal loop prohibits change to the past because the traveller travels to their own past. Their OWN past. THE past. The past that has already occurred.
Since the past has already occurred any travel to the past has already occurred. Any 'changes' made by the traveller have already occurred and so the traveller can have no effect on the past.
In T2 (script) we learn that SkyNet has sent a new model Terminator right after it sent the first one, or possibly right before, just before the rebels took out the Cheyenne Mountain SkyNet mainframe and stormed the L.A. based complex.
So the forty-five year old John Connor of 2029 chooses and sends a specific CSM101 T-800 back through time because he remembers its brutal features and the events of 1994 when he was a ten year old kid. He is doing that which he was always going to do. It was predestined, the future may not be set but for adult John meddling with time travel means that it's not over even when it's over. He's caught, not irrevocably, in a causality loop. For his forty-five year old self the unknown future has only just begun.
The Terminator he met when he was a ten year old kid was sent back through time BECAUSE he remembered meeting it when he was a kid, he sent it because he had to, because it had always been sent. The Terminator that he sends was always sent to the past to stop the T-1000 and it always stops the T-1000 from killing young John.
SkyNet should really know better, it should realise that it cannot change the past because the past has happened and it wasn't changed. Sending something back in order to stop something which has happened from happening in this universe is a futile effort. There can be no changes to the timeline only effects whose causes are yet to happen.
Because John is alive and giving SkyNet hell in 2029 his past is safe because he is alive. John knows that when he sends Kyle to 1984 his comrade will become his father, he knows this because his mother told him. Both he and SkyNet are using the Time Displacement Equipment to bring about the causes for events which have already happened. SkyNet has to send the CSM 101 T-800 Terminator to 1984 because there was a CSM 101 T-800 Terminator that arrived in 1984. It failed, but it still had to be sent because it had already arrived, as evidenced by the existing order of past events, aka history. John has to send Kyle because Kyle is his dad.
Apart from Dyson's death in T2 neither the T-1000 nor John's pet Terminator have much effect on the timeline, rather intentionally from Cameron's P.O.V. I'd wager. But since Both CSM101 T-800s, Kyle and the T-1000 all come from a 2029 where Judgement Day occurred, and have all travelled to their own past, aka THE past, the past of their future, that means that Dyson always died in this way on that day in an explosion at the Cyberdyne building.
Unfortunately for his family, his death, although it was always destined to occur the way it did, was a futile death as SkyNet still bombed the world to hell on August 29th 1997.
T3 messes with this timeline. Not just by delaying the date of Judgement Day but whereas in the T2 Extreme DVD commentary Cameron states that T2 takes place at the beginning of 1994 while T3 tries to convince us that John Connor was 13 during the events of the film.
T3 changes the timeline and the very physics laid down in the previous two films by the creator, ("all hail the mighty Jim"), and in order to be consistent you must play by the rules. T3 plays by its own rules and is at odds with the two REAL Terminator films.
This also applies to the changed future coda in the T2 special edition, since the past cannot be changed and everything before the timetravellers began their chronoportation sequences is consideredd the past for them, the 'unwritten future' only truly begins when John finally defeats SkyNet in 2029.