The loss of something physical has different effects upon different people. Some bounce back easily, others see the loss as completely disasterous and may even kill themselves.
Millionaires sometimes kill themselves when they have lost a lot, but still have more than most people dream of. The athlete may miss a limb more than an inactive person.
I think in that quote Lt. Dan is stating that he no longer sees himself as the person he was, his wholeness, mobility and appearance were a big part of him as a person. He gained a few medals for the act that took his legs and destroyed the image he had of himself.
Then there was the storm and a close encounter with death and the rage at who he saw as responsible. Like confronting somebody who has wronged you, it allowed him to move on and start anew, building a new life and thinking himself complete again.