VoiceAttack uses a standard Windows API method to open the file, which should pretty much equate to putting the path to the file into the "Run" dialog, for example.
If you try to open VoiceAttackHelp.pdf from the installation directory directly, does that work?
Note that because the inline function editor is a third-party component (Scintilla), the F1 key does not open the documentation while that control has focus (you'd need to focus a different control or the form itself, on the inline function window).
Though, I wouldn't expect any reaction, hourglass cursor or otherwise, if you do press F1 on that control.