What worked for me was deleting some files from my computer that had been downloaded the same day Origin wouldn't let me log in. just type in uninstall program into your computer's search and uninstall what you don't want. BE CAREFUL YOU DON'T UNINSTALL A NECESSARY FILE!
Download and install the latest version of Origin at www.origin.com/download (and make sure you have your Origin account ready as well)
Close the origin client and go directly to you origin folder C:\Program Files\Origin Games. Run the origin.exe in this folder with a rightclick -> run as administrator.
Try to deactivate your firewall/antivirus software and/or check the online ports of your connection:
TCP: 80, 443, 9988, 20000-20100, 22990, 17502, 42127
UDP: 3659, 14000-14016, 22990-23006, 25200-25300
For specific instructions on how to open your ports, please visit http://www.portforward.com/ or contact your router manufacturer.
Please let us now, if this problem after this workaround still exist.
Cheers
Basti
