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As I have recalled from the new Doctor Who (2005), during all of regenerations, The Doctor had his full body intact.
Considering a Time Lord has his/her regeneration energy left, from how much damage can he/she regenerate? Can he/she regenerate if I blow out his/her body, for example?
During David Tennant's first appearance (Christmas Special), The Doctor was able to regenerate an amputated hand with leftover regeneration energy from an hours-earlier regeneration. Later, he took a full blast from a Dalek weapon -- which at that time would often completely disintegrate a human -- and regenerated without even changing his face.
Going back further, when Jon Pertwee regenerated into Tom Baker, he was effectively dead (from radiation, as I recall), and the regeneration hadn't started on its own, but required a little "push" from another Time Lord he'd encountered in the same story.
It seems at one point that UNIT was of the opinion that they could kill Missy fast enough to keep her from regenerating, by using seven snipers -- "two shots for each heart, two for the brain, and one extra just for good measure" is the quote I recall -- which would imply there is some level of injury that would prevent regeneration (though whether Missy agreed with their estimate was left up in the air). There was also the original version of the incident in which River Song shot Matt Smith, waited for regeneration to begin, and shot him again to prevent the regeneration (though in fact Matt Smith's Doctor didn't have any regenerations left at that time, anyway).
In summation, I'd say that while there doesn't appear to be a canon statement of how much injury might prevent regeneration, it appears there is some level that would. As always with Doctor Who, however, canon is kind of timey-wimey, wibbly-wobbly.
In "Heaven Sent", the amazing 9th series episode, the Doctor explained what happens when the damage a Timelord receives is beyond regeneration:
DOCTOR: People always get it wrong with Time Lords. We take forever to die. Even if we're too injured to regenerate, every cell in our bodies keeps trying. Dying properly can take days. That's why we like to die among our own kind. They know not to bury us early.
It's not entirely clear what sort of damage the Veil made to him after touching his face, but the Doctor was unable to regenerate and had to crawl his way back to the beginning of the tower to burn his own body and make a new copy. So we can see that burning a Timelord's body also makes it unable to regenerate.
Other examples of the Doctor being unable to regenerate that come to mind is the poison from the Judas Tree used by River song in "Let's Kill Hitler".
So whatever the Veil did to the Doctor, and very specific types of poison can cause enough damage for a Timelord to be unable to regenerate.
In the Series 4 episode of the revival "Turn Left", an alternate timeline exists in which the Tenth Doctor fails to regenerate.
HARRIS: From the evidence, I'd say he managed to stop the creature. Some sort of red spider. Blew up the base underneath the barrier, flooded the whole thing. Over.
OFFICER [OC]: And where is he now? Over.
HARRIS: We found a body, sir. Over.
(Ambulance personnel bring a body on a stretcher.)
OFFICER [OC]: Is it him? Over.
HARRIS: I think so. He just didn't make it out in time.
(As the stretcher is lifted into the ambulance, an arm drops from under the blanket and drops a sonic screwdriver to the ground.)
HARRIS: The Doctor is dead. Must have happened too fast for him to regenerate.
The event originally played out in "The Runaway Bride" in which the Doctor seemed too focused on the Empress of the Racnoss and only chose to escape when he realized he had to save Donna.
Presumably, the water filled up too quickly, or a new torrent of water came out, overwhelming the Doctor and causing him not to regenerate (although there is lots of fire around, so it's possible that it was due to an unexpected explosion instead).
Regardless, this example of the Doctor drowning "too quickly to regenerate" is the only example we have of too much damage to prevent regeneration.
The seventh Doctor's circulatory system was apparently so damaged that he regenerated into the eighth, and even so, the anaesthetic apparently almost prevented him from regenerating.
