If i have 0 runes left and i go to the battlefield that makes me recycle a rune when in conquer, what happens?

Yes — you still conquer and score, and the trigger just does nothing. Sigil of the Storm's "you must recycle one of your runes" is part of its effect, not a cost, so Rule 416.4 applies: you recycle as many as possible (zero), and the ability resolves with no further effect. There's no penalty and no Burn Out — that rule only applies to Main Deck actions. (FAQ 6863 directly covers this.)

One edge case: if you somehow channel a rune after conquering but before that trigger resolves (you'd need priority), you would then be required to recycle that rune.