One account is enough, so let's try some additional troubleshooting steps.
Your device is still enumerating properly so this is likely something we can fix.
When most of your software stops working, often it's some obstructing service that was recently installed. This tends to be firewall or antivirus software, but could be anything. See if you can spot anything suspicious under Programs and Features. I know you said you haven't installed any conflicting programs, but it's good to double-check.
It sounds like Airspace.exe and LeapControlPanel.exe (and VisualizerApp.exe?) aren't launching. When you double-click C:\Program Files (x86)\Leap Motion\Core Services\LeapControlPanel.exe, still nothing happens? None of these applications are visible in Task Manager, not even for a split-second after you double-click them?
Do you have any crash dumps under C:\ProgramData\Leap Motion or %AppData%\Leap Motion ?
Is the service even running? Open up services.msc to check the status of Leap Service. If it is running, great. If it isn't running. cd C:\Program Files (x86)\Leap Motion\Core Services and run LeapSvc.exe --run to see why it's terminating at startup.
When you run Airspace.exe, does it create a file at %LocalAppData%\Airspace\log.txt even if no window pops up? If log.txt doesn't provide much insightful info (it usually doesn't if Airspace.exe crashes at startup), can you run it from the console? The short description of a command to do this is Airspace.exe --enable-logging --disable-gpu --disable-software-rasterizer --skip-gpu-data-loading --v=10 but in This other thread has instructions on how to save that text to a log.