It's possible that once the ageing has begun, it continues rapidly. This would mean that between "old Doctor" and "very old Doctor" may not be that long a time. It could be only 30 or 40 years.
During this time, the Doctor supposedly fights a full-on war because the Papal Mainframe has been taken over by the Daleks. I find it very hard to believe that he could fight a war against a fleet of Daleks with very little backup for centuries.
I suppose we won't know for sure until the Doctor next mentions his approximate age.
Originally Posted by Thamwet:
“My theory is that all of the Doctor's age, but 11 (last body) aged much more slowly, because he was the last. Instead of storing his regeneration energy away for another regeneration, he used his last few dregs to keep his body young for longer.”
I like to think that all his incarnations age at the roughly the same rate (very slowly),
perhaps with ageing speeding up near the end of the incarnation.
With regards to the War Doctor, we didn't get to clearly see him after he regenerated. All I saw was that his hair was black instead of grey. My explanation would be that fighting in the Time War, being immensely stressful, prematurely "aged" the Doctor by causing his hair to go grey (maybe with some more wrinkles). It can happen to humans so I see no reason why it couldn't happen to a Time Lord fighting in one of the universe's most bloody wars.