My wireless mouse has an on-off switch on the bottom site. And yours?

Did it come with batteries? And did you remove the protective piece of plastic that might be inside? And did you measure the voltage of the battery?

If all of the above is fine, try it on another PC or laptop. If you can't get it working there either, it's back to the shop and complain under warranty.

PS. Device manager doesn't say the mouse is working fine. It only says there are no issues with the driver.