You are correct - there really is no way for users of Microsoft Streets and Trips 2007/2008 to know if the program has been muted, just by looking at the screen. It actually is a bit confusing, because you can hear the voice if you press the spacebar, even though the program might have been muted.
One you mute Streets & Trips (intentionally or accidentally), it will always stays muted, even after you restart the program.
There is a little workaround you could use, if you wish. S&T Keys makes sure Streets & Trips voice is enabled each time Streets & Trips is started by F2-key, or by clicking S&T Keys desktop icon.