This must be a Classic Problem, it is almost 2016 and I am having the same problem on Win 8.1 and there appears to be no resolution since 2013.
I have read all the previous postings and they are just like my experiences. I tried most of the suggested resolutions again just in case I missed something. Actually my Sculpt Comfort Mouse worked for more than 6 months then stopped working about a month or two ago, so I expect one of the updates killed it. Now my system starts with no cursor. I see there is a Ver 2.6 of the Keyboard and Mouse Center which I will try. Also there is a note in one of the very good Microsoft info sheets that says the KMC does not support Bluetooth mice installation and that it is necessary to use the drivers associated with the hardware to initially establish the connectivity. Just in case there is a hardware problem with the SCM, I went out and bought a non-Microsoft Bluetooth mouse today and will try it tomorrow as soon as the batteries are charged.
OT: I bought this Acer tablet from Microsoft and it came with a Bluetooth keyboard that works fine with KMC. Since I have no mouse I use the touch screen which also works well. I wanted to upgrade this system to Win 10 but am holding off until I resolve this issue. No rush, the Win 10 November update did not get the glowing reviews that I expected.
I am open to any new ideas that have not been mentioned in earlier posts.