You have 2 separate issues here that are exacerbating one another. One, being a grad student and teaching assistant really legitimately sucks. Been there. It really is pretty horrible for all the reasons you explained so well. Two, you are depressed, which is a physical illness and should be treated as such. Any decent doctor can get you on some meds that will help you snap out of this funk you are in. Sometimes all it takes is a short term dose; some people have to take them for the rest of thier lives.
But that's the key: life. You say you are absolutely stuck, but that's just depression talking. You always have choices. (They might not be good choices, but they're choices.) The first one you have to make, as a personal pact with yourself, is to live. No job, relationship, or grad program is worth dying over.
You may lose face, but you can walk away from your life today and start over in a new town as an irrigation consultant. My point is that when you get to the point where your biological instinct toward self-preservation is being overridden by depression, it's perfectly OK to throw all previous assumptions out the window.
All universities have health clinics. May not be the ritzy kind, but they can hook you up with some meds, which you need, and a therapist.
Finally, tell a friend you trust what you are thinking. Tell your family. Yes, it creates a mess, but it also creates accountability. It means someone is calling and making sure you are keeping that promise to yourself, that you will live and figure out how to do it better, no matter what the cost.