When running the program, the gamepad icon appears in the system tray and disappears when the mouse moves over it. No InputMapper window appears. I've tried uninstall/reinstall, installed older version of InputMapper, and deleted Configuration file in appdata.
The only thing I can think of that would cause this is hiding the notification. To check this, right click on your taskbar click taskbar settings, then scroll down to notification area and click "Select which icons appear on the taskbar".
I've also seen viruses do this to my logitech gaming software and other apps, so make sure you're clean of viruses (use standard apps like avast, malwarebyte's, etc).
Really, these are both shots in the dark and probably aren't the case (you should check anyways though). If you want any kind of troubleshooting please provide more info. See
the developer's sticky post
for what information we're looking for.
In addition I'd be interested in knowing if the application still shows up in the task manager.