I just used Chrome v36.0.1985.125 and was able to login and have an account created on your site using Facebook.
Usually the cause of what you mention is when Chrome has extensions/add-ons enabled that are meant to prevent social networks from working. There are various privacy extension that intenionally block some external sites (Google, Facebook, etc) from loading Javascript on the page and executing. My guess is that you have one of those enabled.
Please try:
* Disabling any extensions you have enabled in Chrome
* Trying from a completely unrelated computer using Chrome to see if you have the same problems.
I hope that helps,
Alex