Humble Bundle disc error: No game disc found! Please insert the sims 3 late night game disc before proceeding.

Did you try hitting play a few times to see if it works ? There are a few users with this issue but I don't know what the solution is.

Try to talk to a game advisor. Maybe they can help you further

The AnswerHQ is about Users helping Users.

Game advisors can be found through live chat.

1. https://help.ea.com/en/contact-us/ 
2. Set your language to US at the bottom
3. Describe your issue with a few words
4. Select Product: The Sims 3
5. Select Category: Billing/Purchasing or Account Management
6. Select Platform: PC
7. Click Find solution
8. Scroll down and click I still need help
9. Click Chat Now to chat with a Game Advisor
   

With Pics here: http://sims3.crinrict.com/en/2012/10/how-to-contact-ea.html