How to Install the game again/PC

I'm trying to register my game but it says the serial code is invalid/already used

You have already registered the game yourself and are trying to reinstall the game
The game does not need to be registered again. Login in the Origin Client with the Email/PW you first registered the game on and download and install the game from there. The game only needs to be registered once and you won't need the code again after your initial registration. This is true for both the DVD and the download version. You can skip the activation step on reinstalling.

Source: http://answers.ea.com/t5/The-Sims-4/FAQ-Serial-Codes-Game-Activation-and-Download-Issues/td-p/4228232

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Give these a try:

The game no longer shows up in Origin

Try the following things: 

• Restart Origin.
• Log out and back in and use the email address instead of the user name. Make sure to use the one you used to register the game in the first place.
• Reinstall Origin.
• Restart your router/modem.
• Make sure the game isn't hidden by accident. To check, put the filter to Hidden Games. If it's there, right-click on the game to unhide ((click on the spoiler below to view an exemplary screenshot))
  
  Spoiler

  
• Get in touch with an EA Game Advisor.

Source: http://answers.ea.com/t5/The-Sims-4/FAQ-Serial-Codes-Game-Activation-and-Download-Issues/td-p/4228232