Hi Louis,
Fortunately, this is easier than I first thought so I'll give it a go without using TeamViewer before we go down the route of trying to work out why TeamViewer won't run.
Open your start menu, and in the search box type regedit, when the results load, right click on regedit and select Run as administrator. From regedit, I would like you to navigate to the following key:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Component Based Servicing
Right click on the Component Based Servicing key and select Permissions. Click Advanced, then select the Owner tab. On this list, click on your username (e.g. Mine is displayed as Tom (Tom-PC\Tom)) to select it, tick the box labelled Replace owner on subcontainers and objects then click Apply then OK.
Now, in this first permissions window, you should see a few entries in the Group or user names: box. Click on Administrators once to select it, then check that the Full Control (Allow) box is ticked, if it isn't then tick it. Then repeat this check for TrustedInstaller. Then click OK, and close regedit.
Download the attached file, louk1_SURT_Fix_v4.reg and save it to your Desktop. Double-click on the file to run it. You will be asked to confirm whether you wish to merge this file to the registry, click Yes. Then reboot, run the SURT, and upload the CheckSUR.persist.log please!
Tom