Modifier Keys stopped working

Since you did a clean install and the problem is still there, the offending setting is probably in your user account. To check if this is the case, create a new user and test with it. If the problem goes away, my suspicion is confirmed. Go back to your regular user account, then System Preferences -> Keyboard. Check the various sub-panes in there, particularly the Shortcuts pane and the Input Sources pane. Either one of those could be configured in such a way that would make your keyboard act oddly.