You should have a much larger base resistors, and one for Q4, and you need a resistor between the emitter and base of each transistor. It might be a good idea to have a resistor in parallel with the LEDs.
LEDs may be visible with as little as 200 μA. Typical current gain of the BC547 is 150, but it could be as much as 800. If the gain is 200, you only need 1 μA to make the LED visible, which is far too small a current, as you have found.
I would say that you should put maybe a 10 kΩ resistor between the base and the emitter of each transistor. The 10 kΩ resistor will mean that the LED won't receive any current until there is about 70 μA flowing in the electrodes.
The base resistors should be 10 kΩ instead of 220 Ω. You don't need or want more current on the base of the transistors, and a 10 kΩ resistor will limit the current to about 1 mA.
I don't know what current the buzzer takes, but maybe some additional gain and some hysteresis would help there.
On the LEDs, the 220 Ohm resistors will limit the current to about 30 mA, which is maybe a bit more than I would have thought you want, especially if the battery is small.