NTE941M Non-inverting OpAmp Has Non-zero Output with 0V Input
Extracts from the NTE941M data sheet: - 


Common Mode Input Voltage Range is typically ±12 V on a ±15 V supply.


This means that if one supply of the op-amp is ground (0 volts) then you must have your input signal greater than typically 3 volts above ground or all bets are off.


Output Voltage Swing (for RL ≥ 10kΩ) is typically ±14 V on a ±15 V supply.


This means that you cannot expect the output to get any closer to the 0 volt rail than typically +1 volt above it.


  any input below approx. 2V yields no change in output


Do you understand why now?