This:
ADC_NEW[0] = analogRead(0);
if( ( analogRead(0) <= (ADC_OLD[0] + 25) ) && ( analogRead(0) >=(ADC_OLD[0] - 25) ) ) //Compare ADC to ADC_OLD
should look more like this (I think)
ADC_NEW[0] = analogRead(0);
if( ( ADC_NEW[0] <= (ADC_OLD[0] + 25) ) && ( ADC_NEW[0] >=(ADC_OLD[0] - 25) ) ) //Compare ADC to ADC_OLD