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.