Apple will replace it if is is covered by warranty or Applecare ( or your consumer rights). They do not supply parts for the device nor cover any data recovery.
Time Capsules usually drop dead from over heating. The internal fan is directed at the Hard drive, it hardly ever turns on, and if it does it just stirs up the hot air inside the device as there is no ventilation.
The fan needs to be modded to turn on more and pointed at the power supply - as this is the part that fails. Specifically it's the capacitors on the power supply. After the faulty components are replaced reassemble the TC with ventilation holes drilled through the base.