Game not running after clicking play button in launcher

@Lilly_Cre  If you're playing on a mac, you don't have to login to Origin, or even have it installed on your computer, to play TS3.  If you're running Windows, then you do have to launch the game through Origin.

It sounds like your computer is automatically moving your Documents folder, which contains your TS3 user files (including saves) to cloud storage.  I'm not sure what exactly the problem is with Origin, but it's easy enough to reset its data.  How to proceed though will depend on your operating system (mac or Windows), so let me know which you're running.

I am running it on Windows 

@Lilly_Cre   Okay, you need to be logged into Origin to launch the game.  However, you don't need to login to TS3 itself, either at the launcher or Main Menu.  Sometimes these logins fail for reasons on the EA side.  But when it's on the player side, the way to fix it is to clear Internet Explorer's cache.  Even if you never use it, the launcher does for some purposes.  Be sure to uncheck the box to preserve data for favorites.

For Origin issues, the first thing to try is clearing Origin's cache.  If that doesn't help, you can uninstall Origin ("the hard way") and reinstall; this wouldn't affect your TS3 install.

https://help.ea.com/en-us/help/faq/clear-cache-to-fix-problems-with-your-games/

https://help.ea.com/en-us/help/origin/origin/manually-uninstalling-origin/

The reason that your saves are disappearing is probably that your Documents folder is automatically being uploaded to OneDrive.  Your game folder is located in Documents\Electronic Arts, and Windows loves to move all of the contents of Documents to cloud storage.  So unless you use OneDrive for other purposes, it's best to just disable it entirely.  You can go in and pull your game folder(s) onto your desktop first if you have saves you'd like to keep.

 I have gone through the hard uninstall of Origin and cleared my cache on internet explorer. I tried to make it so my files are not automatically saved to the cloud, but I'm not sure if I did that correctly. I went through the cloud settings and went to the auto save tab, then went to update folders under the choose which files to protect tab and deselected everything. Is that the right way to do it?

Okay I went and reinstalled origin, but it is till doing the same thing. I signed into origin and launched The Sims 3, clicked on the large blue play button, and then a thing pops up asking if 
I want The Sims 3 to make changes to my computer originating from the hard drive. I select yes, but all that does is take me back to the origin home again.

@Lilly_Cre   That's strange.  Do you have any antivirus/firewall app running?  If so, try disabling it temporarily—just long enough to test whether you can login to Origin and launch TS3 properly.  Also make sure you're running Origin as an administrator.

Another option is to boot into safe mode.  This will disable all background apps while you test Origin.  If you can play, you'll know that something normally running in the background is blocking Origin or the changes it wants to make.

https://support.microsoft.com/en-us/help/12376/windows-10-start-your-pc-in-safe-mode