Ah, okay. You didn't mention anything about a NotifyIcon.
A application gets notified of keys being pressed when the application has focus. When you hide your form and use a system tray icon your application does not have focus and will not be notified of key presses.
If you want your application to watch for key presses when it does not have focus you'll have to write a system-wide keyboard hook--which is not trivial, even in .NET. I wouldn't suggest watching for such a generic key as 'A' though.
Alternatively, you can register a global hot key for a particular window with the WM_SETHOTKEY message, or register a hot key with Platform SDK function RegisterHotKey and process WM_HOTKEY messages in your main Form's WndProc override.