VZ280G How/where may I repair/replace a broken power cord receptor in the all-in-one?

Which AIO do you have? We'll need the full model number like what is show on the sticker that also has your SN and SNID. A lot of the different models have much different procedures for opening the case, and they will each have different parts for replacement.

OK, it's not completely clear to me how the power socket is attached, but it looks like it's in the case with a cable running to the motherboard, though it could easily be the socket itself is soldered to the motherboard. You may have to get inside to look. To get inside you remove that plastic cover over the mount hinge with gentile prying, then unscrew the three screws to remove the mount. The case itself is just snapped together, so again you gently pry the two halves apart. Once the bezel side is off you can access the back and see the motherboard. We want to look at just how the power socket mounts and what might be allowing it loose.

You could talk with a local technician. Assuming the power socket is soldered to the motherboard via through holes, most techs can replace it if they are willing to go through the hassle of a repair rather than a replace.