Why does my Apple Magic Mouse can not connect to a computer?

I have an Apple Magic Mouse 2009. Installed new alkaline batteries. Connect the mouse to an iMac in 2009 with the operating system OSX El Captain 10.11.3.

Mouse worked today, I changed the name of the device in the system settings, and that is all. In a time when I wanted to turn on my computer, the mouse is not connected. The system Bluetooth settings I see my mouse. I can not pair it. After pressing the "Pair", I get the message "Passkey entered did not match". I was choosing passkey "0000" and "1111", but the problem remained. Other devices are connected properly. I tried to turn on and off at different stages, turned on and off Bluetooth, connect a different mouse to work with menus and without additional mouse, etc. What is that?