In Storyline, how can I prevent the Player Next button from working until all layers are visited?

There are a few ways to control the Next button in that situation. They start with disabling Next when the timeline starts on the slide.

• To prevent that from happening if the user revisits the slide, the trigger should include the necessary conditions.

When using Dialog layers (which prevent interacting with the Player options), a trigger could enable Next when all the buttons on the base reach the Visited state. 

Otherwise, use T/F variables to track that each layer has been viewed. Trigger each variable to change to True when the user completes the layer (e.g., they click all the icons, or the timeline ends). Then, on each layer, also add a trigger that enables Next when the timeline on the layer ends with the conditions that all the variables = True.

You can find a file that demonstrates this here: 

TIP: Controlling the NEXT Button 101 | E-Learning Heroes

One thing I'd add to Judy's answer: locking Next doesn't lock the other exits. The player menu is the big one — if your menu lists slides, learners can click ahead and skip the gated slide entirely. Set the menu to Restricted in Player settings, or turn it off for a fully linear course. Same with the seekbar: scrubbing the base timeline never opens your layers, so if your player shows one, treat it as another bypass route to test.

My hand-test checklist for this pattern, in the published output (not just preview):

1. Visit all four layers in any order → Next enables.

2. Return to the slide → Next is still enabled (this is the one that catches most builds — the conditional trigger Judy described handles it).

3. Try the menu and the seekbar → no bypass.

If step 3 fails your requirements, that's when the dialog-layer version Judy mentioned earns its keep — dialog layers block the player chrome entirely.

You can restrict the menu and the seekbar if needed as well