I HAVE FINALLY FOUND THE SOLUTION. All you need to do is uninstall origin completely then reinstall. And I mean delete every single origin file, completely wipe it from your computer and then reinstall off a browser. dont worry you wont lose any data, because its saved in your EA account you can log back in to. I had this same problem!! couldnt find my "product number" anywhere, I wanted to play the sims 4 and finally I figured it out. I realize this is months later but I do hope this helps someone because I felt helpless earlier, and this will help!! just incase, try installing it from a different browser/google login if you use chrome when you install it. sometimes it thinks youre a fraud etc. thats what I did when I reinstalled origin and it worked.
STEP BY STEP FOR ANYONE WHO NEEDS IT! This is for Windows:
1. in the search bar on the taskbar, type in "control panel" and select it/open it.
2. select "programs" and then "programs and features".
3. select origin AS WELL AS THE GAME THATS NOT WORKING! For me I selected both origin and the sims 4. it might work if you only select origin Im not sure. After selecting, click Uninstall and uninstall the program(s).
4. Go to chrome or whatever browser, look up origin and go to their official website and login to your account. Then reinstall it, and it should work.