So after I finished my post complaining about the recent spate of bad luck, I called Dell tech support and actually got to talk to a live person after only about 3 minutes (woohoo!)
I explained the situation, explained how this has happened several times both to myself and people I know with the same computer, and then the operator proceeded to do a troubleshooting process for me. I'm not too upset about that; it's her job, and I was going to end up getting my AC adapter on warranty (no money to pay, yay!).
So long story short (too late), I will be getting a new AC adapter in 1-3 business days. So I just have to live without a computer at home for that long. Taking notes by hand can be tough with my handwriting, but I think I can manage.
We're still waiting on GI bill and daycare compensation, but at least I have a power cord coming. Small victories.