What can be done about a HIGH Ping in Overwatch

I've had an issue similar to this before, and mine turned out to be a RAM issue despite passing every memory scan/test. I finally decided to buy 2 new sticks to use and have not had it since. A good way to check to see if it is a ram issue is to remove 1 stick of RAM at a time (assuming you have more than 1) and see if that improves stability.

When this occurs, I hit Ctrl-Alt-Del which summons that blue screen, and just press "Cancel" which takes me back to the Desktop. The game is minimized, I maximize it and it works again. So I don't have to kill the game, but it's boring.

After reading this part, it makes me think its probably not a ram issue then, since those typically causes the entire computer to crash. This definitely sounds more like a graphics driver issue (or possibly video card overheating).

Running the game in Windowed (Fullscreen) mode will (often) prevent issues linked to alt-tabbing out of the client. Restart the client in Windowed (Fullscreen) mode and try tabbing out again.

An alternative option is to try updating/rolling back your graphics drivers. Lastly, if none of that helps, it's time to file a bug report with Blizzard so that they can look into a fix for it.