The Lazarus Experiment - S3-E6
Revealing mistake: When the Doctor and Martha get out of the elevator and enter the reception room in search of Lazarus, they pass by the string quartet. The violinist and cellist are only miming the actions of playing, as their bows aren't actually touching the strings of their instruments. (00:18:05)
Chosen answer: 1) When Stephen Moffat took over he ignored a lot of what had been developed before (there is not in-universe answer). 2) It would have killed Rose, so the Doctor absorbed the energy. His body regenerated before the energy could do a significant amount of damage that would prevent regeneration.