Your cells are machinery; complex, but no less mechanical for that complexity. Each cell contains all the information needed to create any type of cell in the body, and the only thing preventing researchers from being able to do just that, given a cell and some raw materials, is a lack of knowledge. That lack of knowledge won't last.
The tools of modern biotechnology and the funds pouring into cell-focused fields like stem cell or cancer research will lead to a complete knowledge of our cells sooner than you might expect. People tend to overestimate what can be done in a decade and dramatically underestimate what can be accomplished in two decades - the state of regenerative medicine in 2027 will be impressive, I'll wager, and cancer will be a shadow of its former threat. In the process of getting there, scientists will learn enough about the mechanics of the human cell to create cells of desired types and properties from adult DNA and raw materials. Quite possibly from scratch, too, without the need for anyone's DNA to use as a starting point.
We can see the start of this road today, in the news that turns up every other week in the popular science press:
Stem cell biology takes another exciting leap forward as scientists report that normal tissue cells can be reprogrammed to exhibit many of the properties that are characteristic of embryonic stem cells, including the ability to give rise to multiple cell types and contribute to the germline. These findings [provide] strong support for the rationale that it may be possible to generate stem cells with nearly unlimited potential directly from a patient’s own cells, an idea that has significant implications for regenerative therapeutics.
For the first time, scientists have successfully performed somatic-cell nuclear transfer (SCNT) using fertilized mouse eggs, producing stem cell lines and cloned animals
The defeat of aging, or indeed any medical condition of note, is "just" a matter of replacing, reconfiguring and rearranging cells. The are no obstacles presented by the laws of physics in this matter; a future of perfect health without degenerative aging is "only" a matter of obtaining knowledge and developing the necessary medical technologies. The sooner we start aiming for this goal in earnest, the better.