A Biography of the Doctor
The First Doctor
The Gallifrey Years
The Doctor was woven by the loom in the house of Lungburrow, located in the southern mountains of Gallifrey. He remembered being in the loom. His first memory after being woven was of his 44 cousins laughing at him because of his bellybutton. Cousin Satthrolope consequently smacked him very hard. This belly-button earned him the nicknames wormhole and snail.
(According to Lungbarrow pages 5-6 / Prologue pages 10-12.)
In the Doctor's earliest years, he went through brain-buffing, a rapid learning programme, assisted by Badger, an automation which Cousin Quences [the Doctor's favourite uncle from Time and the Rani] had given him.
(According to Lungbarrow. The Prologue features a scene of his brainbuffing from when he was nearly five and three quarters.)
The Doctor spent much time with a hermit who lived up mount Lung. The hermit taught him much, including seeing the beauty in a flower and looking inside his own mind. He also told him ghost stories including some about the vampires and the Fendahl. It is quite likely that this is where the Doctor learnt both Tibetan and high Gallifreyan.
(The Hermit is first mentioned in The Time Monster and again in Planet of the Spiders and State of Decay, where the ghost stories were mentioned. Lumping in the Doctor's fear of Fendahl stories from Image of the Fendahl is a fairly obvious conjecture, as is the Doctor's linguistic knowledge in Planet of Spiders and The Five Doctors.)
The Prydonian Academy
The Doctor left the house of Lung to attend the Prydon Academy, also referred to as the Time Academy and just "the Academy". Teachers included the later famous Borusa (The Deadly Assassin) and Azmael (The Twin Dilemma), his favourite. One of the teachers was said to have been the only person who understood artron energy (Four to Doomsday). His year group at the academy, the class of '92, were particularly prone to later become renegades. They included Koschei, the Rani, Anzor (Mission to Magnus), Drax (The Armageddon Factor), Runcible (The Deadly Assassin. He never went renegade) and possibly Mortimus and Irving Braxiatel. The Doctor's nickname at the Academy was Theta Sigma (The Armageddon Factor, The Happiness Patrol). He and Koschei built time flow analogues to disrupt each other's temporal experiments.
Whilst the Doctor was at the academy, he continued his studies with the Hermit, who had apparently moved to Mount Cadon. He also played truant to drink with the Shobogans.
(His studies with the hermit are mentioned in Timewyrm: Revelation. Both are mentioned in The Eight Doctors.)
He scraped through the academy on the second attempt with 51% (The Ribos Operation), most of his grades were carefully calculated to just scrape a pass (Lungbarrow page 206/ chapter 23 page 7). However, he failed his chapter certificates in officiating and legislating (Lungbarrow page 207 / chapter 23 page 7) The Master scored higher in cosmic science (Terror of the Autons). The Doctor's knowledge of gallifreyan law (The Deadly Assassin and The Trial of A Time Lord) probably comes from this time, as does his apparently vast technical knowledge. His specialist subject was thermodynamics (Time and the Rani).
At the age of 200, he underwent a major rethink of his life (The Time Warrior). This was probably when he was thrown out of the Academy (Divided Loyalties).
Following his studies, the Doctor stayed on Gallifrey, becoming involved in a campaign to ban miniscopes (Carnival of Monsters and The Empire of Glass. According to the latter, it must have occurred in this period.)
The Doctor was disinherited from his family, although Quences didn't want him to be. Unknown to the Doctor, the House of Lungbarrow loomed a replacement cousin, Owis. (The disinheritance is portrayed in Lungbarrow, pages 171-172 / chapter 18 pages 13-15. On page 81 /chapter 9, page 4 Owis is 675 years old, making his looming 2 years before the Doctor left Gallifrey.)
The Doctor's known sympathies with interventionist groups cost him promotion from his post as Scrutationary Archivist. He had previously worked in the Chapterhouse's Bureau of Possible Events, from which he had obtained an official Prydonian Seal. At about the same time, the Doctor was sent an invitation to Quences' deathday and first encountered the Hand of Omega. Its reappearance set off numerous alarms all over the capitol. The Hand intervened in a fight between the Doctor and his cousin Glospin.
These events finally prompted the Doctor to leave Gallifrey. He slipped into the TT embarkation port on Under-Level 15 of the Citadel, despite agency guards. (Lungbarrow) He had to join in a procession of Time Lords in the last leg of his journey (Nightshade). He slipped into an obsolete type 40, and was soon joined by the Hand, which powered it up and allowed it to breach the Backtime Field Buffers. (Lungbarrow).
The Doctor arrived in the Old Time, herded by the Hand. He encountered Susan, who recognised him as her Grandfather. He didn't recognise Susan. The two left the Old Time and the Doctor eventually came to accept Susan as his own granddaughter. At this time he was probably about 336.
(Vampire Science says he was 1009 at his 7th regeneration and he's been gone from Gallifrey 673 years by Lungbarrow, which is not long before.)
He, the TARDIS, or the Hand instituted several layers of mental blocks in his mind and, possibly, to a lesser degree in Susan. These blocks enabled him to hide his identity and connection with the Old Time. Some of these blocks may have affected his ability to pilot the TARDIS. They may also account for some measure of his apparent senility.
(This is conjecture, but in The Three Doctors, removing the mental blocks apparently imposed after The War Games enables the Doctor to actually pilot the TARDIS. As he was unable to do so before his trial, it makes sense that they removed some blocks that were there from before 100,000 BC. Furthermore, the Doctor is at times ignorant about his connections with the Old Time - as in Cats Cradle: Times Crucible, where he "knows" that he's never been to the Old Time.)