Hello:
I just fixed a PC for a friend that had a "MSE won't instal or update" issue. The second issue not reported to me was Windows Update was not functional.
The PC had two rootkits, found by Combifix [BleepingComputer].
Also BITS [ Background Intelligent Transfer Service (BITS) missing - Microsoft ]
Note: this is how I found Tweaking.com ...
I did not run chkdsk, but i did run SFC via Tweaking.com - Windows Repair (All in One) v.1.95 [setp 3].
SFC must have fixed something because it required a full Restart of Windows.
Then I ran Step 4 successfully. and with only an IP issue [covered elsewhere] all went well, after full restart.
MSE installed, updated, and Windows updates became available.
Hope this Helps,
Regards