Help Me to Identify What I did Wrong with this Circuit
You have very probably destroyed the drive transistor (the one with the collector to the bottom side of the relay coil).

As the is no Freewheeling diode, the first occurrence of the switch turning off will produce a high voltage spike at the collector (given by v = -Ldi/dt) which, under most conditions, will be a high enough voltage to cause catastrophic failure of the device.

I suspect your circuit switched on momentarily and the switch-off would destroy the transistor.

Place a diode (1N400x would be good choice) across the relay coil, anode to drive transistor collector, cathode to positive side of the coil.

See this question as well