And the nuclear fusion is started if not powered by the heat and pressure caused by, wait for it...

GRAVITY!!!

Which is induced by the intense pressure gravity creates in large lumps of mass :) so yeah..

That is not entirely true. Nuclear fission is not powered by the sun, nor are nuclear fusion plants on Earth (when they arrive). However, fission is only possible because of the existence of heavy nuclei that were initially created during super novae explosions in massive stars billions of years ago so you could argue that is is also at least star powered.

The ingredients needed for fusion on the other hand are thought to have been created during the some of the early stages of the Big bang so fusion is truly independent of stars.