Windows 8.1 Update Error Code: 0x80240031

That'd be a negative. Nice try though. 

My process took me through a fresh install of Win8 on a new drive innumerable  times. Using 3 different "Microsoft Accounts", including that of a Microsoft support desk person, who tried unsuccessfully for over 2 hours. 

Get an 8.1 ISO  file, preferably from a trustworthy sourc.

As a work around, I would suggest you to create a new user account and try to upgrade to Windows 8.1 from new user account.

Create a user account.

http://windows.microsoft.com/en-in/windows/create-user-account#create-user-account=windows-8

try another internet connection, it will work. I did that and I have got the update

Man I had the same code error problem where I have tried to update so many times and all wast of time , and recently I have tried another internet connection from my friend account and the update worked. I have 8.1 now, keep trying different isp connection and it will work with you.

http://answers.microsoft.com/en-us/windows/forum/windows8\_1-windows\_update/error-code-0x80240031-windows-81-update/77d7171d-3fc7-4150-9c32-14c8643ccf52

Try the above method. It should work