@krystinaconnect First, the easy part: when you install content through the launcher, the splash screen is often hidden behind the launcher. If you have a second plumbob in your dock, that means the launcher is installing the content (or trying, anyway), and you can click on that plumbob to see the progress.
The bigger issue is that your laptop's hardware is below the minimum requirements for Sims 3. That doesn't necessarily mean you can't play, just that the game might not run very well. As a first step, try unplugging your monitor and just using the laptop screen; I'd like to know whether it works.
If it doesn't, try setting the game to windowed mode. Open Documents > Electronic Arts > The Sims 3, open the file called options.ini (TextEdit works), and cmd-F to search for fullscreen. Set the value to 0 instead of 1. Then see if the game opens.
