How do you choose the desired input before starting Skyrim?
I found a setting in SkyrimPrefs.ini
that you can define before starting Skyrim.
Under [MAIN]
section bGamepadEnable=0
disable the joypad bGamepadEnable=1
enable it.
I had the same issue, it automatically picky my Gamepad as input on first starting Skyrim. There was an option called "360 Controller" in the System->Settings menu, after disabling it Skyrim defaults to mouse and keyboard on every start.