emitter to base amazing transistor effect
Perhaps a more interesting question is why the LED is 'off' under some conditions. You've made a kind of expanded Darlington configuration, which means the current gain is the product of all the current gains. Normally the current gain of one transistor is of the order of 100. 

Since transistors have leakage you might expect that the leakage of the first transistor would be multiplied by 10^8, so even if it is &lt;100pA it will turn the LED on. 

The reason this circuit does something interesting (respond to the base of the first (top) transistor) is that the gain of a transistor is not constant with collector current. It drops both at very high and at very low current.