I think that the cord of your mouse "which is very thin" is damaged from the place where it enters the mouse. This happened with all of my friends including me twice. When you try to pull the cable from the mouse, it will blink, then will go away again.
If this is the problem, you will need to open the mouse, cut the cord from just above the place where it enters the mouse, then cut the cable just before it exits the mouse. Then solder the wires, and it will work.
As I said, try this: move the cable and pull it, push it, and do everything, from the place where it enters the mouse. I am almost 90% sure that this is the problem as I have experienced this many times with A4 mice and once with Logitech MX500. The problem lies in the cable, the place where it just enters the mouse.