If you cast High Noon, you’ve already cast at least one spell that turn (High Noon itself) so you won’t be able to cast any more spells until the next turn. If High Noon enters the battlefield on a turn where you haven’t cast any spells, you’ll be able to cast one spell that turn.

If you cast a spell that was countered, you can’t cast another spell during the same turn while High Noon is on the battlefield.