You don't have your zone down... how long have you lived there? the reason I ask is that during the winter, basements are notoriously cold and damp. Humidity might not be a problem for you for very long.
There are some very low light houseplants... but I don't know if they'll take away smells, but they'll add some good air. Take for example a plant called "Mother's-In-Law Tongue" or Cast Iron Plant... cuz nothing kills it. :D Its latin name is Aspidistra elatior
There are some other low light plants, understorey tropicals sometimes don't need a lot of light. But really, you will have trouble cuz most plants need some amount of sun and lights, unless you spend some serious $$. Just won't do well.

start doing yoga

Go outside into the sunlight as often as you can. Do some research into the condition called SAD to find out why.

Some indoor plants will help provide more oxygen for you and clean up the atmosphere a little.

Several bowls of water placed in strategic places throughout your home will help to hydrate the air you breathe. You can put some essential oils into the water to help with your depression. Try Lavender, Bitter Orange or other citrus, Rosemary, Basil, Bergamot, Chamomile, Clary Sage, Geranium, Jasmine, Lemon Balm, Neroli, Patchouli, Thyme. Or burn any of these in an oil burner, or use diluted in water as a room spray, or add them to potpourri.

Frankly, if my home affected me like this, I'd be very keen to move elsewhere ASAP. It's worth considering, at least.

Here is a link that might be useful: SAD

Daturaeater...your post made ME SAD. Maybe what you are smelling is mold??? No wonder you are depressed. Get out of that basement where you can have some sunlight and grow some plants. I'm hoping that is a possibility for you....

A couple of inexpensive shop light fluorescent fixtures will provide enough light for many houseplants, including things like spathiphyllum, gesneriads (i.e. African violets), begonias etc. If it really is that dry in the basement it sounds like you could use a humidifier (overall, this sounds like a poor living environment - can you move?).

Here's some info on light and how it affects mood. Suggestions include a light box and getting outdoors as much as possible (a long walk or more vigorous exercise every day could be helpful).

There've been some other good suggestions here; depression can be a serious illness requiring prompt medical attention, so think about seeing a doctor just for diagnosis. You don't necessarily have to take an antidepressant (St. John's wort remains controversial. It has been found effective in some studies for depression, but probably isn't a good idea for moderate to severe depression, especially if one is self-medicating).