If you kill Brynhildr before his when you play resolve, does when you play not work?

Yes, Brynhir Thundersong's "When you play me" ability will still resolve even if Brynhir is killed after the ability has been placed on the chain.

According to FAQ #6035, once a triggered ability has been put on the chain, it resolves regardless of whether its source permanent is still alive. The game only checks if the ability's specific instructions can be followed (such as targeting requirements or location references).

Sequence of Events:

1. Play Brynhir: You perform the "play" action. Brynhir enters the battlefield and her "When you play me" ability triggers.
2. Trigger on Chain: The ability is added to the chain as a pending item.
3. Brynhir Killed: An opponent kills Brynhir. She is moved to the trash.
4. Resolution: When the chain resolves, the ability executes. Because the ability does not require Brynhir to be on the board to function (it simply applies a global effect for the turn), it resolves successfully.

Important Nuances:

• Independence: Triggered abilities are independent of their source once they are on the chain. As long as the ability does not require the source to be present to resolve (e.g., it doesn't say "deal damage equal to my might"), it will function normally.
• Effect: Once the ability resolves, the restriction ("opponents can't play cards this turn") is active for the remainder of the turn, regardless of the fact that Brynhir is no longer on the board.

Note: I could not fully verify the claim regarding the inability to react to units entering the battlefield against the retrieved rules.