I've had my internet go out, and I'm still able to play Sims 4 just fine.
What will/should happen is Origin will ask you to login with username/password. There will be an Orange banner at the top of the Origin sign in saying: Online login currently unavailable.
Type in username/password and then it logs into Origin in offline mode. And should be able to play game from there. There will be a banner up under the Origin menu that says Offline Mode. The games you have already installed should be available to play. Click Sims 4, it should be ready to play as normal.
As for it not responding. I'm not sure why that's happening. Maybe try closing out of Origin. And login as shown above.