Well... if you're not getting +5V on the connector, fuse F1 does indeed look like the cause.
A logic probe helps a lot diagnosing which pins are high, low or changing. Much more accurate than a multimeter.
All Amiga ports except the phono connectors for video and audio have a power pin, that's why you have to be careful to plug in things that are "Amiga compatible" with the power off.
Ideally. I daresay people have come a cropper before with 2 player games and switching out the mouse for a 2nd joystick. Although joysticks usually don't need power, maybe it's only an issue for controllers that do need power.