found it in C:\Users\Admin\AppData\Local\Temp\WUDiagTempFolder. It contains two files: dism.log and output.txt.
Looking at the two timestamps it seems that would have been for a subsequent problem report.
Yours was 3:23 PM. This one was 10:23 PM. Oh. Same minute. So I suppose this lets us infer your local timezone? <eg>
Get WU Exemption info failed? Looks like some kind of permissions problem? That could also explain your other symptom. I would really prefer to have a ProcMon trace guiding me before making guesses about "solutions" based on common symptoms but I suppose
it might be safe to try a bit more of the same that you have already tried...
So your new symptoms just seem to be more symptoms that your WU client is broken. Here is an example of a procedure that Server admins were using on their clients for similar symptoms
http://blogs.technet.com/b/sus/archive/2012/09/05/additional-note-on-kb-2734608-regarding-wsu-windows-8-and-windows-server-2012.aspx
Note a new wrinkle suggested in a comment involves deleting the main WU registry key (and expecting that WU will regenerate it, perhaps with better permissions.)
Otherwise when I search support for SoftwareDistribution this is still the main hit:
http://support.microsoft.com/kb/971058/en-us
You say you have already tried that? Did you only do the manual procedure or did you try using the FixIT? The manual procedure looks ridiculously obsolete but I don't know if the automated one is any better. E.g. perhaps it is exactly the same thing but
done under the covers so you don't see whether anything useful is being done (or whether silly things are being done.) Note that you would have to select your OS first before downloading it. And since the procedure requires you to be an administrator to
run it, e.g. at least do it from an elevated cmd window, I would also try elevating the IE window that you start it from. I suspect it would be best to save it and execute it as the Administrator, perhaps even in safe mode, although then the services might
not be running or be allowed to run.
It hints at an "aggressive mode". Have you seen that and tried it? With all possible precautions that you are doing it as an Administrator? E.g. maximum authority and as little interference as possible.
Otherwise my guess is that your WU is broken in such a way that the troubleshooter misses it or the authority being used by the troubleshooter is different from that needed to do the install. Etc. Then, again, I would be running ProcMon to try to find
out what all the symptoms are and clues about what they mean.
HTH
Robert