Make sure you deleted the right folder: C:\Users(username)\AppData*Local*\Arduino15. The folder used to be C:\Users(username)\AppData*Roaming*\Arduino15 so you might have deleted that one instead.
W4KRL:
Here is the arduino_debug output for 1.6.9.0:
The output didn't show up in your post
One thing you could try is to use Arduino in portable mode. To do this you just need to create a folder named portable in the Arduino IDE installation folder, then restart the IDE if it's running. You will need to redo File > Preferences after doing this.
I don’t understand your instructions for the portable mode. Do I create the folder within the arduino distribution folder? I tried that and nothing new happened.
W4KRL:
Do I create the folder within the arduino distribution folder? I tried that and nothing new happened.
Yes, for example if your Arduino IDE was installed at C:\Program Files (x86)\arduino-1.6.8 then you would create the folder C:\Program Files (x86)\arduino-1.6.8\portable. This would help if the IDE wasn't able to write to your Arduino15 folder for some reason but from looking at the error log I suspect it's a different problem. You can go back to non-portable mode by deleting the portable folder.
I prepared a portable version of 1.6.8 on a memory stick. It runs just fine on my laptop and another desktop - all in Windows 10. But it acts badly on my trouble machine - splash screen then nothing. Obviously, the problem is with the computer, not 1.6.8. I've uninstalled Java - same result. Reinstalled Java - same result. Run registry cleaners - same result.
At this stage, I am looking for any solution short of doing a clean install fo Windows.