Computational biochem student here. Unfortunately we do not have the technological prowess to replace parts of our body as they age. Researchers are working on growing whole organs from the extracellular scaffolds of cadavers, but this technique is in its infancy and I would take all news concerning it with a grain of salt.

Unfortunately, we are limited by which organs and tissues we can replace. Case in point: we cannot transplant the brain. Intracellular and extracellular buildup (eg. amyloid beta, lipofuscins, etc) will cause inflammation and cellular damage, and there is no way to remove them. Loss of telomeres and the accumulation of mutations leads to the breakdown of the genome, which is the host of the majority of a cell's state information. We ARE computer programs, and the moment memory gets corrupted things start to break down and behave improperly. The probability of any one of an unlimited number disease states in a cell correlates also with the level of misfolded, degraded, improperly tagged or trafficked gene products, which will always increase with time, even if the central program is well-behaved.

Remaining at homeostasis requires us to not reach chemical equilibrium, which requires we consume a ton of energy. Converting the necessary molecules during cellular metabolism puts our cells under heavy oxadative stress. Living requires a substantial number of evolved countermeasures, but eventually it will all catch up to us.

Why then are we so inept in our understanding of biology? The sheer astounding complexity of our biological machinery is not matched by any other problem that faces us. Biotechnology is amazing, but we are vastly limited by what we can do outside the context of in vitro techniques or simple, sacaled down in vivo assays. The real systm is always too complex to fully understand, and with so many unknowns we are essentially flying without radar. We can study proteins, promoters, etc. (slowly and with great difficulty) but we cannot "repair" them. We can't excise a damaged region of the genome and replace it at will. You would probably be shocked to see what techniques are actually even available--with my own limited experience it often feels like we are blindly throwing darts at targets that may not even exist. Our sequence information gives us clues, but we lack structural information (especially post-translational modifications) or knowledge of interaction details in the biochemical pathway.

If every physicist, computer scientist, mathematician or engineer stopped what they were doing and began work on this problem we might make some headway. Right now our hands are tied. This is absolutely the most important and complex problem in the world. We need the transcriptome, proteome, interactome, complete structure data, better algorithms, faster computers, higher resolution imaging (spatial, temporal, etc), better techniques, higher througput, I could go on and on. We certainly haven't entered the industrial age of biotech yet...

Do consider giving biology a try. We could use you and everyone willing. If you want to live twice as long, not get cancer or Alzheimer's, or cure any important infectious diseases, you should join us. Especially if you're a logical and abstract thinker.