I have designed the Hbridge with the BJT BC108 to drive the motor which draws 400mA current. But it does nothing when I connect the motor in the terminals of H bridge. When I remove the motor and check with LED it worked fine but not when motor is connected.
Datasheet of BC108 specified that it can withstand up to 500mA of current. So I think it is not a problem.
However, as your transistors do not have gone away after connecting the motor (it still can light up the LED then), it means that you do not give the transistors the proper bias (base currents).
With your motor, and the re-selected transistors, you have to calculate the base currents in order to make them saturated when opened.