Since this is a general, hot-end does not heat up thread, I wanted to say that I had a similar problem.
My print failed and the extruder stopped heating up. I was on a short deadline, and was panicking. I needed to get a lot of printing done by Tuesday (for a city meeting, making architecture models for a project), and our TAZ4 failed Sunday. I called every electronics place and they did not have 4.7Ohm 7w resistor. What we found was this http://deezmaker.com/store/#!/Heater-Cartridge-for-3D-Printer-12v-24v/p/35812047/category=0
a shop in LA that was open on Sundays (cool hacker space that make 3d printers). Their printers use this heater catridge instead of a resistor. I bought this on a whim because I needed to get the printer running the same day. They sold me one of those things for 10 bucks, and I sloppily soldered it in place of the green resistor. https://www.lulzbot.com/products/heat-resistor-47-ohm
I also ordered the green resistor, but they came in way later than the Tuesday deadline. Shipping and order processing took the better part of a week.
Several weeks later, the cartridge heating element still works even though it fit a little loosely, and the hot end heats up much much faster as it is a 40W one. I calculated the resistance on it and it’s around 3.7 ohms with current going through it I think. I haven’t replaced it with one of the original green resistors.
When my resistor failed I forgot what resistance it was reading, but I think it failed in an open circuit, and I might have been getting a reading of 0, but I’m not sure. I read that if a resistor fails it can fail in either open or closed circuit. Read what https://forum.lulzbot.com/viewtopic.php?f=36&t=104&p=11633#p4040 said to trouble shoot though