Hello
Is the mouse the only bluetooth device that won't connect? Can you try to connect the mouse with another computer if you have one? It sounds like the issue might be with the mouse.
Make sure batteries are good, and installed correctly (positive/negative are placed correctly). If it is a brand new mouse, make sure the protection tape is pulled out from the batteries.
Otherwise perform a reset on the mouse (you would have to refer to Logitech instruction how to do that), this is especially important if the mouse has previous paired with a different device.