Someone else reported going back a month in restore points: https://www.reddit.com/r/Windows10/comments/4egyrg/windows_10_april_updates_kb3147458_and_kb3147461/d21715g
Did a system restore to before the update (yesterday), system restore was successful, but no change to the operation of the computer.
Restarted system to go to Safe Mode/attempt another system restore and Windows installed KB3147458 again.
Error message somewhere in this process it gave a failed to install an update when doing restarts.
Attempted a system restore to farther in the past (04/02) but it failed with error 0x80070002.
Tried going through and killing processes of any background applications, no change.
Tried disabling all of the startup processes, no change.
Checked installed updates, saw that KB3147458 was installed again, uninstalled it and deleted contents of SoftwareDistributionDownload to try to prevent it from reinstalling. Seemed to be successful, but computer was still broken.
Things I wanted to do but could not:
Access Services (window opens but hangs empty).
Access Windows Update (never opens (ms-settings:windowsupdate, the wait operation timed out) or in safe mode (immediately closes).
We're out of ideas other than reinstalling Windows (which seriously shouldn't be the answer).
Do you need my logs?