Thought I might offer some suggestions - this is a real strange bird, to be sure.
Remove Avast completely. Let Windows Defender protect the PC for now.
Uninstall it from Add/Remove Programs. If you have difficulty uninstalling it, see here:
Avast Uninstall Utility | Download aswClear for Avast Removal
Please follow the instructions to boot the system into safe mode to effect the removal properly.
Let's make absolutely sure the system is not infected, so please run these two tools and post the logs using the "#" code box:
So the newly-created administrative account is corrupt? Please go into this account, open an admin command prompt and enter the following code:
This will place a text file on the desktop called sfcdetails.txt. Please also post that file.
findstr /c:"[SR]" %windir%\Logs\CBS\CBS.log >"%userprofile%\Desktop\sfcdetails.txt"
This is strange. Normally, I would expect just the opposite.
Until we get this resolved, please turn off auto-hide taskbar.
Please type reliability history in the search box and open the Reliability History tool. Post a screenshot of the most recent day with a red X on it, showing the errors below - widen the columns if necessary so we can read them.
Let's see if there are any clues in here.
Graphics drivers could be an issue as well. Open Device Manager, expand the Display Adapters, select your graphics, right-click and select update driver>search online. See if anything installs that way. If not, go to the OEM support site, and check there as @essenbe suggests.