Time Lords (or at least properly educated ones, so perhaps not the Doctor) can voluntarily stop both their hearts and be fine. Romana demonstrates this in "Destiny of the Daleks."
DOCTOR: Romana. Ha ha! I thought you were dead.
ROMANA: Well, the only way to escape the Daleks was to feign death. It's lucky they didn't know I was a Gallifreyan.
We see the Doctor survive having one heart stopped in The Shakespeare Code (Martha restarts it shortly after)
We see another in The Power of Three
RESEARCHER: Hospitals are logging a global surge in heart failures. Cardiac arrests.
DOCTOR: That's it. Oh! Oh! Oh! Only one heart. Other one's not working.
It seems this ...
This exact scenario occurs in the Eleventh Doctor story "The Power of Three" (Series 7, Episode 4). In that episode, a bunch of black cubes from space (cosmic cubes, if you will) mysteriously arrive on Earth. Their purpose is initially unknown, and the people of Earth eventually forget them, using them as paperweights and such. After a year on Earth, the ...