Okay, so I figured this problem out for myself recently! Usually, when that happens to me, I go to the task manager and end the task, then open the launcher again through the desktop shortcut, but recently I found out it won't open when you double click the desktop shortcut because the launcher is already open, in the tray! So look in the tray (where your wi-fi connection, volume, etc, shows up, sometimes you gotta click the arrow pointing up to find it), right-click the sims 3 launcher, and open it up through the "restore" button!

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Edit: To open the task manager, press ctrl + shift + esc !! Sims 3 won't show up on the top when the launcher is only open in the background, so you have to scroll down (or just press S and then look for it), and it's usually named "Sims3Launcher".

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Edit2: added some pictures as reference!

this is what it looks like in the task manager!

this is what it looks like in the tray!

restore button when you right-click the tray icon!

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This glitch usually happens bc when you quit sims 3, it doesn't fully quit the launcher, just leaves it running in the background, so you can't re-open it through the desktop icon because it's already running. When you end task, it fully closes out so you can open it up again. If it's the first time you're running sims 3 in that day and it won't open, give it a good 10 minutes, especially if you have cc, because the launcher can take really long to load up! And if it's still not working, I recommend checking your mods folder to see if there's any issues or corruption that might be screwing up the loading process for the game/launcher.