[EA app] I cannot launch ME3 (2012)

I bought Mass Effect 3 somtimes around june 2017, via install disk. I still have the disk at home. I've played more than 500h. Both my N7 account and my EA account can prove that I own the game. I've last played it a few months ago, during N7 day where I played a few multiplayer games.

However, since yesterday I cannot access my game anymore. When I start it, a pop-up window shows up. I have migrated from Origin to the new EA App as soon as it released and I've played ME3 since then so it can't be tied to this.

Can't post the screenshots from the windows as this post don't seem to accept them, but here's a summary of what they say:

1. Pop-up window I got when I booted the game.

- We could not activate ME3 on this computer with the associated Orign account. Please find your product key and activate the game with your Origine account.

- Enter product key

- If you have already done the registration, please make sure that you are connected with the same Origin account you used to activate the game.

- You are logged under the ID: ...

- Log with a new ID

- Buy the game

2. Widow when I clicked the "Enter product key" tab

- We are sorry, an error occured.

- Your computer is currently offline. To activate your game on this computer with your Origin account, you must first be connected to internet.

- Retry

- Quit

3. Window when I clicked the "Log with a new ID" tab

- Activate your game

- Please log with your Origine account to Activate ME3 on this computer

- invalid email address or password.

Needless to say, my computer was connected to internet (I was speaking with friends on Discord when I got that pop-up) and both my email and my passwords are correct (I just used them to log on the support website).

My problem now is how do I play my game? I tried to repair the game, it didn't fix it, I tried to reinstall, it didn't fix it.