Update - 9/8/15
Fixed by reinstalling Windows fresh (Again).
I think the problem was caused by installing Windows linked with my Microsoft account and then switching that to a local user. My Microsoft account was registered for the insider program so perhaps I was receiving the fast updates and switching to a local account put me on slow updates which got Windows Update muddled in the confusion.
Windows Update appears to be stuck/broken. It displays this loading animation even when left alone for an entire day (See screenshot). All the other panels such as Windows Defender will display their available options, it is only Windows Update that will not show.
This is a clean install of Windows 10 Home.
I have made some alterations to the service configuration, disabling what I had been advised as unnecessary services. I have reverted as many of those changes as I could remember but it is a possibility that one of those changes caused this.
Background Intelligent Transfer service is "Running" and set to "Automatic (Delayed Start)".
Windows Update service is "Running" and set to "Manual (Trigger Start)".
8 Aug 15 - Edit: I have cross referenced services with another computer with an unaltered fresh install of Windows 10 Home. No difference in service configuration was found.
Internet connectivity is stable. Network profile is "Public". No alterations have been made to the default network configuration.
User account was originally associated with Microsoft Account but was then switched to be a Local Account.
Have run sfc /scannow which found and fixed some problems. Running sfc /scannow a second time reported no problems.
Running the Windows Update Troubleshooter through Troubleshooting -> Fix problems with Windows Update yields no results. "Troubleshooting couldn't identify the problem"
Have deleted contents of C:\Windows\SoftwareDistribution\Download. Have also re-initiated the C:\Windows\SoftwareDistribution folder.
Have ran command "Dism /Online /Cleanup-Image /RestoreHealth" which reports no errors.
Have ran command "Dism /Online /Cleanup-Image /StartComponentCleanup /ResetBase".
Have ran the fix-it from https://support.microsoft.com/en-us/kb/971058 which reports "Troubleshooting couldn't identify the problem"
Cross-posting this from my question on Microsoft Answers which unfortunately did not garner much attention so I'm trying on these forums.
8 Aug 15 Edit: Checking installed updates, I do not have KB3074683 or KB3081424. Manually downloaded and installed both of these updates. Did not fix the issue.