The power cable is connected and the power light is on, but nothing happens when I press the power button to turn it on. I have also tried holding the button down for ten seconds. I bought my Asus x205ta four months ago so it is relatively new.
I was wondering if you have already tried powering on the laptop only on battery, i.e. without connecting it to the power adapter?
If that didn't help and the Power button doesn't respond either, because the laptop is new and is still under warranty, I would suggest you to take it to an authorized service center and get the issue diagnosed by the certified technicians.