Since I have no idea where you live, I am not sure what options you have for the issue with your landlord and the faulty furnace. I know here, there are both local and state offices that will deal with complaints/issues of this kind. Landlords generally have a set of standards they are required to follow as far as safety, living conditions, unresolved problems they are responsible for, etc., in return for keeping their buildings as rentals, keeping tenants, and having the rent money paid. Maybe you could call your city offices to start with and explain to them what has happened and they might be able to tell you just what you need to do. You do, after all, have documentation with your huge and sudden overuse with the electrical spike so that is on your side.
This is the best I can come up with, but hope it might give you an idea of where to start. I agree - do NOT go on the warpath, but do NOT let the landlord walk on you or get away with not maintaining the property. I am fairly sure you don't have a money tree to pay your rent and bills with, right? Good tenants are hard to come by, I know that from past experience as a landlord. If you are a good one, pay your rent on time, then they should do what is necessary and right to keep you. I prided myself on taking care of my properties and my tenants, so I was lucky to have great ones. Fair is fair though. Good luck and I hope you get this resolved quickly. By the way, if you DO have a $$$$ tree, could you send me some seeds......