LM2902N short circuit
The input circuit of an LM2902 won't be damaged if it is shorted to ground.  Remove the short and the circuit should work properly.  If it doesn't then try using one of the other amplifiers.  If the opamp is damaged, then the input may have experienced a negative transient of over voltage condition.  The LM2902 has PNP transistors at the input (see diagram).  There is a small leakage current coming from the inputs.  Yes, if you measure a high impedance on the inputs there is a chance the inputs are not damaged.