Your plants are electrotrophs.
In your cold, dusty world, airborne dust can accumulate large amounts of electrical charge. Since your world (is it the same world?) is so cold that methane is liquid, the atmosphere is mostly hydrogen which conducts electricity even worse than ours. Huge charge differentials accumulate in the air before finally equalizing via immense lightning bolts.
Your "plants" take advantage of this by offering the charge an easy way down. Plants extend as far up as they can reach, and put out branches with many ramifying tiny spikes. The spikes glow with corona charges / a.k.a. St Elmo's Fire most of the time (as depicted above) - they are collecting the atmospheric charge and giving it a path to ground in exchange for a little work on the way. Thus your autotrophs fix chemicals in such a way that heterotrophs can eat the chemicals and take advantage of the stored electrical energy.
In dense growths the corona charges from these towering plants are enough to light your dark world.
I can feel a comment coming - yes it is from L.Dutch - and he asks how a sunless planet can have wind. That is a very good question. This rogue planet is spinning extremely rapidly and the atmosphere does not quite keep up with the planet below. High winds result. Thus the ultimate source of energy for this world is the rotational momentum of the planet itself.