A lot of people seem to have issues with x-input controllers, myself included.
The specific symptom is that the game seems to recognize you are using a controller, but not actual input (any buttons or sticks) is registered.

The solution I'm using is mapping keyboard and mouse to gamepad.
There are plenty of free utilities that let you do that (antimicro/antimicroX being an example)
I wanted to share the mapping I'm using, since there seems to be no convenient way to check controls.

START - ESC - menu
SELECT - ENTER - for selecting menu items

LEFT STICK - W/A/S/D - movement
RIGHT STICK - MOUSE - freelook

A - E - use/transform
B - F - lamp
X - SPACE - jump
Y - TAB - map

D-PAD - ARROWS - menu navigation

LEFT TRIGGER - LEFT MB - bank left in bird form
RIGHT TRIGGER - RIGHT MB - bank right in bird form

Hope it might help someone to have the same enjoyment out of this game as I had