restarted imac but magic mouse not working

Hi. I've returned home and restarted my iMac and the Magic Mouse won't work. Bluetooth keyboard connected ok so I could log in but the mouse does nothing.

I've connected the cable from iMac to mouse for a few hours to recharge with no result. Turned the mouse on and off and held the left and right clicks for several seconds again with no result. The mouse and iMac are only 6 months old.

I've stabbed at a few keys and done unintentional things so I know I can control things that way but don't know any keystrokes to navigate to preferences or to the bluetooth icon to see if I can connect that way.

I need help please. Can anyone give some suggestions?