Each cell divided from your original ovum/sperm combination. Those came from their parents, which came from their parents, etc. etc.
Cells have been proven to be able to divide into new ones FOREVER, given minimal changes. Telomeres and the other forms of aging are all just anti-cancer techniques.
You do however have a good point when you mention the brain.
But that is also not insurmountable. It's called gradual replacement. Kill about 1% of the brain every year and grow new cells.
Yes there will be some partial memory loss. So what? By that age, you already have memory issues. Personality and the 'soul' (if it exists) will remain the same. You ameliorate the memory issues by leaving personal recordings of important things - video, etc. Basically, you look at your own Facebook page [ ughh, I found a real use for Facebook
You are correct we will never win against entropy.
But you are wrong when you think the constraints are freer for artificial intelligence. They simply are not there. The 'weaknesses' of organic life are actually strengths that people do not understand. Things like blinking - it is an automatic health maintenance procedure, not a weakness in human vision.