No, the game doesn't start. It just says "EA servers are currently not working" at the beginning and the game exists afterwards. I already wrote what the EA support answered me.
Well, that sounds like a connection Problem.
First, if you only want to play the single player game you can do that regardless, set Origin to offline mode and if that still not works disable your internet connection.
Now the game should work.
If it doesn't work, create a DxDiag, also go to your Reliability monitor (Press the windows key and "R" at the same time and copy or type "perfmon /rel" (without the quotes) in > ENTER) and look if it has ME3 entries.
If yes double click at the last one, copy it to the clipboard, (Bottom left corner) save it to a text file and load it up like the DxDiag with the "choose file" button at the bottom right corner of the reply window.
Additional if it is a connection problem:
Restart your router.
If that not helps, shut down your Windows firewall and disable the real-time scanner of your antivirus software. (just for testing purpose, don't forget to activate the firewall and the antivirus software later on.)
Should it work after you disabled the firewall, here is a description how to allow a program to communicate through the firewall
If that not helps here is a EA connection troubleshooting guide.
