The Doctor does succeed in changing history in Genesis of the Daleks. The events of previous Dalek stories, if they happened at all, are now vastly different. The Doctor delays Dalek development by 1000 years, but, more importantly, his actions cause Davros to remain alive.
The Doctor's warnings about the dangers of the Daleks had some effect on their creator, making him paranoid enough to activate a force field in his chair. He thus survives the Daleks' assassination attempt. In the previous time line, Davros was killed and forgotten. Davros also remembered some of the Dalek defeats mentioned by the Doctor. For example, the Daleks retain an interest in Earth and want to invade it again, especially as Davros thinks he knows how they were defeated.
The Daleks, unaware that Davros survived their attack, leave Skaro as soon as they can, going out into space and abandoning their homeworld. They either exterminate the Thals when they leave the bunker or note with disinterest that they have already gone. Embroiled in a war with the Movellans, a group of Daleks return to Skaro many centuries later (Destiny of the Daleks). Davros is, however, taken prisoner by humans, and the Daleks are forced to fight the Movellans without his help.
The Movellans win the war with a virus. Ninety years later a detachment of surviving Daleks rescue their imprisoned creator (Resurrection of the Daleks). The Daleks recognise the Doctor, perhaps from their tactical survey of Gallifrey. This faction is led by the Dalek Supreme, and they have returned to Skaro, perhaps hoping to recover information and equipment left behind.
One hundred years later Davros arrives on Nekros, his programme to turn humans into Daleks already well advanced. (Perhaps when interrogated the Doctor told Davros of the events of Evil of the Daleks, leading Davros to conclude that if the Daleks possess some of the 'human factor' they will not be slaves to logic, and will not be drawn into an impasse as with the Movellans.)
Skaro is known and feared by humans as the Dalek homeworld, but the creatures are not regarded as being an overwhelming threat. (In this time line the combined Draconian/human peace is strong enough to encourage such complacency.) The Supreme Dalek arrests Davros (Revelation of the Daleks) and tries him.
On Skaro, Davros wins the arguments regarding human tissue and mentality, and takes over the white/gold Daleks, augmenting them and himself. He becomes Emperor (perhaps again trying to duplicate a successful pattern described by the Doctor). However, some Daleks rebel over the issue of racial purity.
They learn of the Hand of Omega and leave Skaro to retrieve it and use it to threaten or destroy Davros. Both factions use their primitive time corridor technology to return to Earth in 1963 (Remembrance of the Daleks). Skaro is destroyed by the Hand 1000 years before or after (according to the Doctor) - probably after, putting the date of its destruction somewhere around the 30th century. Davros is left in space near Earth in 1963.
Prior to Genesis of the Daleks, Davros did not feature in Dalek history and was never referred to. Without him the Daleks had a solid, cohesive empire, always with one purpose. With him around they are a mess of squabbling factions, incapable of the unity needed to develop dimensionally transcendental time travel. Whilst Davros lives the Daleks will remain disorganised, and will never become the threat that the Time Lords so feared.