I have been lurking on Hacker News for a little under eleven years now and have just now created an account, for whatever this is worth.
Within my own life, I've noticed a similar pattern to the one you've described: when I have felt low, such feelings have often coincided with me not feeling that productive at work. Perhaps I'm working on working on a project that isn't particularly motivating. Perhaps I've hit some technical snag that requires me to reconsider my approach and/or implement some inelegant solution that triggers my perfectionistic tendencies.
I'll now project some of my own thoughts / feelings about this stuff that may or may not resonate with you (perhaps they'll resonate with some other reader, though). As another commenter has already pointed out, I think a lot of this causal link between happiness and productivity (I think the causality is bidirectional, too), is conditioned in some way. Specifically, I think this sort of depression arises when we fail to live up to some internally-held, idealized image of ourselves. Having some standards to live up to is probably healthy, although, if the standards are too high or unrealistic, then neuroses will follow. For context, I'm drawing a lot on Karen Horney's ideas in _Neurosis and Human Growth_. If this diagnosis makes resonates, then the solution is to diminish the role one's idealized self plays in one's thoughts and actions, which diminishment probably involves a lot of mindfulness and also some sifting through of one's "shoulds". What are the top ten things that you're thinking of doing? For each of those things, consider: is this something that you think you should do, or it something you actually want to do? If the former, continue to introspect: why do you feel like you should be doing something you don't want to do.
Obviously, there's some things we all must do that we probably don't want to do. I think with work, though, it's very easy to become disconnected from what you actually want. If you don't like what you do on some fundamental level, or something feels off inherently (even if this feeling is unconscious), you'll probably begin to dissociate / compartmentalize in some way which might contribute to your underlying feelings of depression.
Again, I'm assuming a lot, here - maybe this applies, maybe this doesn't. Whatever the cause, I wish you the best in dealing with it. Life's too short to take too seriously :).