Sims 3 Store Downloads won't Install

@karategal49314  Just as an experiment, please try downloading into a clean user folder.  Move your entire Sims 3 folder out of Documents > Electronic Arts and onto your desktop, open the launcher to spawn a clean folder, download one item, and click Install.  The splash screen can be behind the launcher, so you may not see it, but if the install process is working, you'll get a second plumbob in your dock.  You can click on that to see the installer working.

And if you don't get a second plumbob, close the launcher and reopen it, then try to install again.

Unfortunately, that didn't change anything. 

It may also be worth noting that the game itself doesn't always start when I click the play button in the launcher. Sometimes, instead of the game starting, my Origin window just pops to the front of my screen, and the launcher itself either does nothing or closes. When this happens, I have to close Origin and the Sims 3 launcher and reopen the launcher. If I already have Origin open when I open the Sims 3 launcher, this seems more likely to happen. The fact that pressing the "install" button from the downloads screen also brings up the Origin window about 50% of the time makes me think that the two are related, and this may be an issue with the new 64-bit & Metal Sims 3 version. Unfortunately, just closing Origin and the launcher and restarting the launcher doesn't seem to be enough enable me to install my store items. 

It's weird because there's not even an error message or anything. It just.... doesn't seem to do anything. Maybe there's some check where it needs to verify that I have the game in Origin, and it's failing at that step for some reason.

I figured it out. On the times that I'm able to start my game from the launcher, the launcher closes and reopens, and I have to press start again before my game actually opens. On the automatically re-opened launcher, I'm able to install the downloads.