A human being is like a computer. Within our DNA is the memory of every single ancestor- that includes EVERYTHING.
You are confusing science with Assassins Creed. Nothing is stored in your DNA of your memories, they all reside within your brain (some knowledge might be transferrable via DNA (i.e. hereditary), but it's no more than basic primal responses (think insects)).
Theoretically it should be possible however to replace all the dead cells with new living cells. This is something your body does every day, so you should be able to do this with nanobots while supplying the body with oxigen and nutrients artificially. The only problem is that the cells in the brain have specific links with eachother that form a complex neural network. If all the connections were still in place, you should, theoretically, be able to copy it entirely and replace the dead cells with new ones.
Although it seems very unlikely that it is possible, there is no real reason (other than the degrading of the brain cells) that it could not be done.
Just think about it for a moment, organ transplants are relatively common place now, in some time (and some stemcell research later) we can grow our own organs to replace the old ones. This is something that there is no doubt on that we can achieve within a limited time. If you can replace and regrow organs, you can grow and replace random cells. If you make nanobots, they could be placing new cells where the old ones were and remove the old ones. Although a bit of a stretch, it is feasible with science we are exploring today (it will be a very long time before we can do anything of the sort, but it seems to be an attainable goal). Why can you not scale up this process to an entire human body?
As I said, the only thing that might be a problem is the degeneration of neural cells, once their connections are untraceable, the information is lost. If you enjoy the computer metaphore, you can reconstruct all the hardware, but if you cannot connect it properly, it won't work. (Not software, the implementation of the software is the positioning and interconnections of the hardware (i.e. the neurons)).