wireless rechargeable mouse is dead

Wireless rechargeable mouse just died; iMac won't recognize an older battery-type wireless mouse. What to do? Computer is inoperable..

Wireless rechargeable mouse is completely dead... tiny light does not come on when attempting to recharge.

Turning computer off and on, it does not ask to connect to the battery-type wireless mouse despite new batteries, little light on mouse flashing...

Help? Thanks.