Something should have happened when you had the nail in the electromagnet,
and broke the circuit after it had been connected for a few seconds:
the light-emitting diode gives a little blink.
This is interesting, because one battery isn't supposed to be able to
operate the LED at all.
If the circuit still doesn't work
Make sure it is put together correctly. It
should look like the photograph.
The two wires from the electromagnet are connected to the two wires from the
LED, and also to the two wires from the battery -- except that the battery
is only briefly connected and disconnected.
Remember that the wire is covered with clear insulation. We sanded oit
off of the ends of the wire when we made the electromagnet. The electrical contacts must be made in this sanded-off region.
The blink is not very bright. It might help to dim the lights in the room.
Try reversing the light emitting diode (or the battery)