If electrons flow very slowly through a circuit, why does it not take a notcieably long time for a lamp to glow when you turn on a distant switch?

Because you don't have to wait for the first electron that entered the circuit
to come out the other end.  The first one that enters the circuit bumps a
different electron, then the one it bumped travels a short distance and bumps
another one, and so on and so on.  The physical speed of each electron along
the wire may be slow, but the bumps move along much faster than that.

Another thing to consider:
I don't know what the actual numbers are. 
But let's say that the electrons moved through the wire at only 0.000001
(one millionth) of the speed of light.  Even if you had to wait for the same
electron to move from your end of the wire all the way to the light bulb, it
could still arrive at a lamp that's 984 feet away in 1 second after you flip
the switch.  Over any realistic distance inside your house or school, do
you think you'd actually notice the delay ?

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