First things first... have you checked the battery in your mouse?? Both to make sure it has enough juice & that it's properly seated in the well - NOTE: make sure you use alkaline batteries, NOT those cheapo "super duty" batteries sold by $$ stores. The Sunbeam alkaline's work great, there's several reviews on utoob.
Did your Keyboard / mouse come as a set?? -- If yes, have you checked to see if they support Unifying technology?? -- Unifying keyboards / mice have a orange / black star on the bottom near the model number. -- It's on top of the receivers (see attached) - In order for the unifying receiver to work with more than one device, you need to download the Logitech Unifying software here... http://support.logitech.com/en_us/software/unifying -- very compact & easy to use
NOTE: not all Unifying keyboards / mice come with a Unifying receiver. - Good example is the M310 mouse, it supports Unifying technology but comes with a dumb receiver - I have two of them, speaking from personal experience. - Cannot get them to work with the "dumb" receivers they came with. BUT, they work just fine with both Unifying receivers I have.
Hope that helps -- good luck!