the OP said:Do you think it has sense that the problem is because of having input before power supply ins connected?
What I would do, is take the other 1/2 of the OP amp and configure it as a buffer, but put 10K resistors in series with both inputs. (connect output to the inverting input through the 10K resistor). The point (I1), then goes through the 10K resistor to the non-inverting input.
This is an "automotive" type of environment, so some sort of transient protection is necessary as well.
Bypass caps were not shown on Mike's schematic, nor was some sort of "disabling" the other 1/2 of the IC.
At least, I think there are two of them.
See if Mike has any other ideas.