There is no extrapolation from the computer industry. But quite simply there are a number of animals that don't appear to age significantly (they die of natural causes but without the death rate increasing with age), and plenty of even more extreme examples in the plant kingdom, of trees apparently thousands of years old. So there doesn't appear to be a fundamental problem with maintaining cells in working order, indefinitely.
Over evolutionary timescales though, organisms that evolve and adapt will always tend to outpace biologically immortal organisms, and as the other respondents correctly state, there is no evolutionary imperative to survive much beyond childbirth (and it is likely even a negative in evolutionary terms to linger around competing for resources with your children).
However, if people decide that regardless of the above, they want to live forever, I think it is biologically possible, and once someone finds some real traction on that problem, it will happen.