Failed firmware upgrade
I've read several different threads about similar problems with brand new NEX cameras, and the cause usually turned out to be that the owner was anxious to use his/her new camera and didn't give the battery time to charge fully. I don't think anyone tried to download firmware right off the bat, but there were different problems with the camera locking up and in general just not working right due to the battery not being charged all the way.
It's entirely possible that Fuji would do the same thing; i.e., not work properly due to the battery not being fully charged. And, there is an internal battery that gets its charge from the removable battery, so that may be an issue as well...if the main battery wasn't charged, then the internal battery probably didn't get charged all the way either.
Please don't take this the wrong way, but since your post indicates the problem occurred the same day that you got the camera in the mail, I'd be inclined to think the initial lockup problems could be caused by the battery not being fully charged. Did you make sure the battery was charged all the way per the instructions before you attempted the firmware download?