Connecting the blood supply and other organs are already completely possible. It is also possible to keep the brain alive for hours outside the body.
Remaining concern is the spine and the 12(x2) nerves which connect to either side of the brain. http://en.wikipedia.org/wiki/Cranial_nerves
The largest one of them all is the spine, the spine has 46 tracts
I have read that people do forearm transplants and regain full nerve function (after 5 months), the brain works more like USB, but this is only months after, and our nerve reconnection technology, at least that used in practice is not that advanced to perfect it yet, in fact it's merely in it's stone age, yet it is taking huge steps as far as the articles i've read. Although many new improvements are being made every few months.
Then there's organ printers, which could perhaps be used to scan a cross section of your spine and that of the donor (skydiver/ a body grown in an artificial womb), then ask the computer to grow a model that connects the nerves accurately so that you could go home the same day with full function. Harvard med head says that spinal cord nerves could be grown and even made completely genetically yours, within 10 years from now already, don't know how the printer will connect the nerves together though, however it happens naturally so we should be able to mimic it somehow, do we already know how?
i am posting this because i think that if it were to be made feasible, that it would show t be the absolute greatest invention and benefit to man kind that had ever or even will ever be done. As this would grant us immortality and a quick cure to all diseases, aging and much more. Not only this but it would be of astronomical benefit to the economy and progress too.