OK, if this is true, then pick any kind of organ transplant as a result of a death (not caused to get said organ).
All major transplanted organs have to be "alive" which necessitates a live donor, That would include heart, lungs, intestines etc. Usually kidneys and partial liver transplants might be ok as they usually do not kill the donor, although the probability of compromising their health is great. Why transplant dead organs from a dead donor that can't work? As Nadir said, brain death was invented to allow harvesting of organs from live, compromised patients.
Corneas are harvested from actual dead people because they do not survive on circulating oxygen but derive their oxygen from the external air - hence they are still useful from a dead patient. Skin and bone can also be used from cadavers.
If anyone needs more info I would look into Dr Paul Byrnes' website.