Go to the arrow pointing upwards in the bottom right corner, there should be a origin symbol on there, right click the symbol and press "Quit Origin", then open origin again and it should work.

If that didn't work here is another method:

Close Origin completely by right clicking the Origin system tray icon and selecting Exit.
Make sure that Origin is up-to-date.
Make sure Time/Date is correctly set on the PC.
Reset Internet Explorer Settings (even if you don't use IE, Origin does).
Untick the options in the LAN Settings.
Clear Origin Cache Data.
Reset the Windows Host File.
Reboot your computer.
Flush DNS.