You mean the cable that lets you mount the Chromecast not physically on the TV? That has nothing to do with it. It's just there if, in your installation, there's no space for the Chromecast to stick out of the HDMI port on the TV.
Try orienting the Chromecast differently - vertically, horizontally pointing toward the router or at right angles to it. Since there are no external antennas on the router, you can't move them around, but you could try standing the router on its front edge (lean it against the wall).
Put your phone near the Chromecast and run
SignalCheck Lite on it to see what kind of wifi signal you're getting where the Chromecast is. If it's bad there you may need a longer HDMI cable to be able to put the Chromecast where there's a good signal.
If there's a good signal, and the Chromecast updated when you installed it, it could be defective. See if you can swap it for one you can try in the store.
(I'm using the Chromecast app to mirror my screen, and one of my grandsons uses his Chromebook to play on the big screen - but the Chromecast is only a few feet from the router, so I don't know how sensitive it is.)