If you look at the door hinge you will see the Yellow spacer bearings that the outer door runs on.
As is the case with most Dysons, it is just a matter prizing the inner door over the edge of that Yellow bearing, but at the same time, being careful not to put too much pressure in the brittle plastic. It will jump out with a bit of bending in the end. Then access to the screws will be easy for the hinge to be removed.
David
February 2012