Have you been able to get any other Bluetooth devices (ie. headset) to work with your computer? If you have access to a headset, you can try syncing with that. If it doesn't work, it might be your Bluetooth chip. Otherwise it might be a faulty mouse and you can try to exchange it for a new or different mouse.

You should also be able to check the BT settings in your system's BIOS to see if it's active.

That's all I can think of...