You are not alone. Several have had the same problem with no resolution. I think it has something funny to do with the User Accounts. Making a second account with admin privleges doesn't work. I would try to reinstall the OS from the hidden image and try again. A Refresh like Dell tried will not do the trick, as it retains much of the data from before the Refresh; you need a clean start. Don't do anything witht the Admin Account other than let Windows set it up and set your password. All updates need to be installed before the upgrade will show in the Store. I have upgraded five Win 8 installations and have had zero problems.
I purchased a Inspiron 17 7737 directly from dell.com on 12/5/2013.  It was delivered on 12/182013.  It had Windows 8 as the operating system.  I had assumed that it would have the latest version of Windows when it arrived since 8.1 had been issued in October. I opened the Store app and the upgrade to Windows 8.1 was not available to me.  I understood that this was a problem for others and did not pursue it further at that time.  I was out of town for 2 weeks in January and did not use the laptop during that 2 week period.  When I returned, I opened the Store and found prominently placed the invitation to the free upgrade to 8.1. I was signed in using the Administrator account and when I hit the download button for 8.1. I was given the message "You need to use an account with Administrator privileges to install Windows 8.1, try logging in with the user account of an administrator of this PC and try update again".  I verified that my account had Administrator privileges and tried again and got the same message. I created another user account and gave it administrator privileges and tried the download again signed in on that account and got the same message.  I called technical support and for over 5 hours over 2 different days, the technician attempted to resolve the issue by uninstalling and reinstalling Windows updates. When that failed to resolve the problem, he "refreshed" my PC which, I understood put it back to the status it was in at time of delivery. He then had to do all the Windows updates (approximately 65) and tried to download 8.1 again.  This did not change the error message when trying to download to 8.1.  At that point, I was told that they were elevating it to a technical team who would research all the logs from my machine and come up with a solution.  They indicated that they would call me back when a solution is found. Although my Administrator account was not recognized when attempting to do the 8.1 download, it recognized the Administrator role when the technician needed administrative approval to do all the uninstall and reinstall activities when trying to resolve the issue. Has anyone else experienced this problem?  Has it been resolved and, if so, how was it resolved?  
Store does not recognize my Administrator User account when attempting to 
upgrade from Windows 8 to Windows 8.1