So you downloaded the game through the EA app, but then at some point it just said it isn't downloaded? Or was it right away?
Have you ever played the game? If not, would you be able to simply delete the entire game and reinstall it? You said that there is no space on your PC - before you downloaded the game, did your PC have the minimum space requirements that are listed in the required specs?
Did you move the game files from the place that the EA App downloaded them to? Could you check if the place that the game is currently located in your files, is the same that is specified in the EA App? As in, could you go to the EA App, go to settings, downloads, and see if the installation path leads to the place that the game is located in?
I would also recommend doing the App Recovery for the EA App, just to see if that helps with making the game appear downloaded.
- Pythia