The Doctors age:
During William Hartnell's time as the Doctor he was something like in his 600's and Tom Baker referred to himself as being in his late 700's. Sylvester McCoy was nearly 1000. Matt Smith should be something like 1,200 (the Impossible Astronaut states that would be his age when he was 'killed') Obviously one year real time is not the same as the Doctor's screen time.
This still leaves 600+ years for the first incarnation which as Dave says is unusual.
Either there were more, The Doctor did a good job looking after himself or...
Toward the end of the original run, the seventh Doctor referred once or twice to a triumvirate of Gallifreyans who set up Time Lord society - Rassilon, Omega and 'The Third'.
This was something that would have been built upon had it continued on air, but cancellation stopped that, although the story was continued in the now non-cannon Virgin books. This culminated in Lungbarrow, which saw the Doctor return to his actual home on Gallifrey, and in flashback we learned of the trio. In it the implication was that (surprise) the Doctor was The Third.
After the war with the Great Vampires the Gallifreyans needed to recover and reorder. Rassilon set up the society, while Omega stellar engineered stars, which led to time travel. The Third helped recreate the way the now Time Lords reproduced, which was artificially through a vast genetic machine, knitting bodies together, giving them the ability to regenerate.
He then past through the device and became The Doctor.
Although the books are non-cannon, if they use that kind of route, then maybe the Doctor/Third could count the years previous to passing through the genetic machine.
What idle speculation eh?
