Sims 3 won't launch and Origin won't install

I've been having issues with launching the Sims 3 for a few months now - Origin constantly asked to install updates every time I launched. I stuck with it and updated - but now when I click on the Sims 3 to launch, nothing happens at all. It's not appearing in my processes in task manager, and Origin no longer seems to be installed on my computer. However, when I try to download it, it claims it's there (I just can't find any files relating to it at all). If I click to continue the install regardless, it just doesn't do anything. So I can't launch, can't install and generally can't play it. Any advice? I must admit I'm a bit fed up with Origin/EE at this point - it's been a truly rubbish service for ages.