I was just going to post about using a car battery. I have this set up for my hunt camp 2 large car batteries from a deisel and a 1000W inverter.
One thing though is you don't need to go to an inverter, just run straight from the battery to 12 volt LED bulb sets. They are easy to get automotive or on line. Likely get a couple months before needing a recharge. Down the road you can always add a solar pannel and charge controler with a light timer but it would likely cost a couple hundred bucks to get set up.
I have power to the coup but am using a small light with about 20 LEDs in it for two 4x5 pens. Turning it on 4:30am, its not a lot of light but so far layers are keeping up with an egg a day 9 days out of 10. when it gets cold I may switch to a regular bulb just to take the chill off a bit. Pretty common to get into the -20s to -30s here by January.