If the cable broke or lost tension I would expect it to shift into the small ring since that is the direction the spring is tensioned. Unhook the cable completely and then try to move it by hand and see if it moves freely. Then while the cable is unhooked hold it tight in one hand and shift between gears and see if the tension on the cable increases and decreases properly. This should at least allow you to narrow down which end of the equation the problem is.