I can absolutely relate to what you have written. I feel that I have absolutely shutdown too.
Is there any way that you can discuss the fact that you manage SAD with your course tutors, in order that you receive the support and additional time that would enable you to submit the work.
From my own experience, it is absolutely essential that from college/uni's point of view - they are made aware of what the problem is and how it impacts on your ability to study and submit coursework.
In terms of keeping things together. Perhaps if you can concentrate on the basics until the worst passes, i.e. getting enough rest, eating well and trying not to beat-up on yourself for being unwell.