Origin "download" button doesn't works

@echuize  If you're running Windows, you can try clearing Origin's cache, or even uninstalling and reinstalling Origin itself (the hard way), which wouldn't affect your installed games.

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/

When you uninstalled the game, did you clean your computer's registry before reinstalling?  If not, you might have remnants of the previous install, and those remnants could interfere with your attempts to launch the game going forward.  You can clean your registry manually or with a tool like Piriform's CCleaner (free).  Here's where to find the registry entries, if they're still present:

https://help.ea.com/en-us/help/the-sims/the-sims-3/manually-uninstalling-the-sims-3/

If none of this helps, clear Origin's cache again, and then run it as an administrator—right-click on the Origin icon to see the option.

If you're on a mac, please say so, as you'd need to try a completely different workaround.