Sounds like you may need a newer furnace if it has a pilot light, they haven't had those in many years. You may save a lot of $ getting a newer one.
They all operate basically the same, somehting has to light the burner(s) and open the gas valve. Most of the electronics are safety and timing, there are safetys that will shut off the gas if the valve opens but the temperateure doesn't come up assuming the flame is out and things like that.
A gas furnace doesn't need a lot of power, the blower mostly, you could easily power with a small generator.