Thank you all for responding!
I thought the advice for using a meter was good so I tested the wiring. The meter readings were not really making much since, so I was able to determine that whoever had it before me did mess with the wiring for some reason. I re-arranged the wiring and finally got it to work! I tested it with a cooking thermometer and it now properly cycles on and off to maintain the set temperature, problem solved! Thanks again for the suggestions!