Coco
So the good news is that you know that Hood works when provided with power.
That suggests that there is no power in wore coming out of wall.
I presume you have no multimeter.
It is best not to go for trial and error as it is dangerous, but here are my first suggestions:
See if you can work out what each of the FCU are for and label them.
Switch OFF power at FUSE box (Using Fuse box is now essential as you now have no idea where the power is coming from to power that wire - it could even be from the lights).
Reconnect Cooker hood to wire out of wall.
If the 13A fuse has not blown, then changing it from 13A to 5A will not make a difference - they will both pass power (until they blow).
If you are lucky then the 13A fuse currently in the FCU has blown, and if you change it to a working fuse (or 5A or 13A) it will make it work.
So try using the 5A fuse out of the plug, by swapping it with the 13A fuse in the FCU.
Switch ON power at FUSE box
Cross fingers.
SFK