It happens when the Internet is not working, you'll see a red glowing light on the router.
To fix the router, drag one of your peeps on top of it and they'll work on fixing it. When the light turns green, it is working properly again.
Another instance this could happen is when there's already one person sitting down using the computer and someone else in the house is going to use it. They could be on the other side of the house but if their action changes to "Browsing Web" or anything computer-related, the game knows that the spot is taken. There's only room for 2 people to use the computers.
Good luck!