USB Mouse Disconnecting/Unrecognized

Specifically, my problem is with the Logitech Trackman Marble. I have two of them, and they are both having the same issue. I long thought it was a problem with the usb cord, but it now seems that it is in fact an issue with the mouse itself.

The problem began some years ago, but was minor enough to ignore for a very long time. The mouse would disconnect, usually when jostled, and then promptly reconnect. Over time, it got worse, sometimes requiring a great deal of fiddling with the cord or plug to engender the reconnect, and then even necessitating that the cord be placed at an elevated angle to maintain a connection, or swapped around into different ports, etc. Eventually it reached the point where it was disconnecting every few minutes, and then eventually refusing to reconnect even after extensive maneuvering.

Now it has reached the point where the mice are not being recognized by the computer at all. (They don't even show-up in device management anymore.)

I have uninstalled and reinstalled the driver, checked them on a different computer to make sure the issue is with the mice and not the laptop, and even replaced the usb cord on one of the mice with another mouse cord. After the cord was replaced, the mouse worked perfectly for a day and a half, but then it proceeded to go through the intermittent-cutting-out-to-eventual-complete-non-recognition process that initially took several years, but this time over the course of a single evening. Now neither of the mice are being recognized when I plug them in at all.

None of my attempts to find a solution have turned-up any information about other people having this same issue, or at least seemingly not the same issue because none of their solutions (driver reinstallation, laptop updates, turning off the power-management feature, etc) have helped me.

Since this style of mouse has been discontinued, I am extremely eager for any solutions that will help me keep my favorite mouse of all time functioning. Thank you!

@andrewsawesome took this one right after I opened it to swap the cords; it's the only one I have on my phone right now. I'll take the mouse apart again and upload some more useful ones when I get home from work.

Thanks for taking a look!

Here are pics of everything. If there is anything you think another angle or anything can help you see better, just let me know. And thanks again for looking!