Power cord connection issue---we have tried

This failure might not be in the power cord but the internal power supply. If your LCD is older then 15-18 months for sure it needs a power supply replacement.
Symptons of a failing power supply are:
1- Set does not powers ON.
2- Turns OFF by itself.
3- Needs to be unplug to make it powers ON again.
4- When the set is ON, it produces a humming noise through the speakers.

You can find a power supply replacement visiting this website and you should be able to replace it yourself.