That symptom looks like what I saw when I had not disabled auto-reset on the Arduino UNO running ArduinoISP. The Arduino bootloader uses the same protocol as the ArduinoISP. The bootloader will return the signature for an ATmega328P but then it will return 0 if you try to read memory or fuses.
Did you connect a 1 to10 uF capacitor from Reset (+) to Ground (-)?