Hey,
I was just trying to purchase FC3 but I had an interesting issue. I added FC3 to my cart and went to the shop (cart) page then logged in using the fields on the left.
It seems, however, that the login state is not staying put on the shop page. It still shows me the login boxes on the shop page, but if I navigate to the other pages on the site I get the "You logged in as..." text and buttons. When I go back to the stop page, I get the login inputs again.
This issue is affecting Chrome 26.0.1410.64 m (Adblock+ being the only installed extension).
When I switched over to Firefox (17.0.1 - slightly out of date, I know, I don't use it much) the store worked fine and I completed my purchase, and the purchase showed up in the (still logged in) Chrome afterwards.