does seat of power trigger if you move onto forgotten monument on your 2nd turn? (no conq)

No. Moving onto Forgotten Monument on your 2nd turn can't score or conquer, so Seat of Power's "When you conquer here" won't trigger.

Forgotten Monument's "Players can't score here until their third turn" prevents the entire scoring action — including conquering — before turn 3, and no conquer means no conquer triggers fire. You can still move a unit there and establish control, but since scoring is prevented, no Conquer occurs (see the Forgotten Monument FAQ ruling).

One more thing: Seat of Power's ability says "here," so it only triggers when you conquer Seat of Power itself — conquering anywhere else wouldn't trigger it regardless of the turn.