The socket shown in the photo is of a snap and lock DC power connector. (If by happy accident you should happen upon one, snap and lock power cables are identifiable by the presence of one or two wide arrows in the plastic covering molded over the plug ends.) Many manufacturers use -- or have used -- this type of connector -- Dell and Toshiba, just to name a couple of the largest.
Mind that this is not the same item as the superficially similar 4 pin mini-DIN connector used in low-power cables for audio, video or serial data. The pins on the snap and lock are thicker than those on the mini DIN, and are arranged in a more four-square, less trapezoidal layout. This is done to prevent introducing, say, 100 Watts to components designed to handle less than one Watt.
I mention the disparity because suppliers will incorrectly refer to the connectors as DIN or mini-DIN. Here's an example, in a Third-party Gateway replacement.
In any event, without a schematic or pin-out and power specifications from the manufacturer, ensuring the proper polarity and voltage across the connection is problematic.