Since you've already shown that the mouse USB doesn't work with either a mouse or the keyboard, try getting a new mouse. Or at least, get a new cable for the USB. A better option;, many mice and keyboards come as a set and work with a single wireless USB plug in the back of the computer. Both devices use the same wireless USB plug. Give it a try.
Next, if you haven't already, be sure to replace the batteries in both the mouse and keyboard.
Hope this helps
I have a problem with my mouse, when i turn on PC mouse led for few seconds turn on and then turns off. And when after startup mouse still dont work. btw keyboard works, for keyboard i have different that usb cable. (idk how to name it) But when i tried another keyboard with same usb cable as mouse, keyboard didnt worked too only few seconds and then turns off, same like mouse. (Keyboard that worked usb was like circle but that mouse and another keyboard was basic usb cable rectangle)
Here is a video - https://youtu.be/3ksJAxSyQtg
Thanks and have a good day!