First check the outlet with a night light to ensure there is
power there. Then widen the router plug that goes into the
outlet. Your outlet may be loose & not contacting the plug. If
the plug is "V" spread out a little more, it will touch the metal
contacts within the plug.
Also you can see if your router turns on in another outlet -
preferably in a completey different room where your certain it
is not the same electrical circuit in the house.