ADC0820 and piezo drum pad
If you are using a raw piezo input, its output is a charge rather than a voltage.  It is rather like a capacitor which is being charged and discharged by the flexing of the sensor.  Your input to your ADC is basically floating, attached to a capacitor when the drum is quiet.  When you put the scope on it, the probe impedance discharges the piezo sensor.  You will need a resistor to ground sufficient to discharge the leakage current on the input of the ADC, which is spec'd as +/- 3uA.  You may want a resistor divider anyway between ground and Vref so that your ADC can see negative swings.  Note that a big hit will generate a voltage exceeding your Vcc, so you may also need some protection.