A Type 50 TARDIS was the TARDIS that the First Doctor used prior to his life as a renegade Time Lord. (AUDIO: Prisoners of Fate) The Doctor decided to steal another TARDIS, a Type 40, when he finally departed Gallifrey with his granddaughter Susan Foreman. (TV: The Name of the Doctor)
The Type 50 was angry and hurt it had been spurned by the Doctor when he stole his Type 40, an inferior model, and called it miserable and dilapidated. The Doctor would later claim he had to take the first available TARDIS he could find and he was reluctant to tell anyone why.
The Type 50 TARDIS later escaped Gallifrey on its own, suffering damage in its escape as it attempted to go after the Doctor. The TARDIS had to jettison 9 tenths of its interior to escape, and travelled to Valderon, where the Doctor encountered it during his fifth incarnation in 3556. By that point the Type 50 TARDIS was so badly damaged it couldn't leave the planet, or so it claimed. In fact it was capable of moving short distances.
The TARDIS was in pain by the time that it encountered the Fifth Doctor again. Sibor had discovered the TARDIS's capabilities of looking into the future after it had granted the people of Valderon with the Miracle, where everyone could speak with a different language. However Sibor decided to use the TARDIS for her own gain, putting it in a prison for 20 years and giving it just enough power to stay alive. According to the TARDIS Sibor tortured it to ensure its obedience. But she didn't realise the TARDIS was showing her possibilities of the future to find the right person to repair it.
During this time the TARDIS just wanted to return home, but it generated a strong telepathic field to find someone who could repair it. The TARDIS revealed it had manipulated events so then it could feed off the energies of paradoxes to rebuild itself. The TARDIS was later destroyed when it became trapped in one of those paradoxes. (AUDIO: Prisoners of Fate)