HP Pavillion all-in-one will not power on . The power source is good

[Tonyb38]

The power cord is good and the green light in the back comes on  but the computer does not come on. It is out of warranty.

[itsmyname]

@Tonyb38 --  the computer does not come on. It is out of warranty

The power-supply (the part inside your All-In-One) is required to deliver different voltages to different components.

So, while it is lighting-up that lamp, it might not be supplying the other voltages to the other components.

Or, your computer's motherboard has failed.

Or, your computer's processor has failed.

Trouble-shooting the above possible failure-points is something that should be outsourced to a certified computer technician.