DIAGNOSIS This is almost always a power supply issue. The internal fuse on the Pop's main PCB may have blown, or the external power adapter is faulty.
FIX Unplug the power adapter from the wall and from the back of the machine. Inspect the adapter cable for any cuts or kinks. Firmly reconnect the adapter to the machine's DC port. Plug the adapter into a different wall outlet, directly, not through a power strip. The white LED on the power button should illuminate immediately.
IF THAT DIDN'T WORK The 24V DC power adapter itself has likely failed. This is a common point of failure. You must contact Nespresso Customer Service for a replacement adapter. Do not use a generic adapter; the voltage and connector polarity must match exactly.
HEADS UP The Pop has no user-serviceable internal fuse. Do not open the housing. If a new official power adapter doesn't solve it, the main control board is dead and the machine requires professional repair or replacement.