thanks for your answers. Some comments in advance for your upcoming tests with the new device:
1) even if the connection of Ref made no difference in your previous tests, Ref must be connected to GND (or another stable, low impedant voltage), it must not be left floating for correct operation.
2) taking away the input capacitors is ok. But if you take away the input resistors the input stage of the amplifier has no path for the bias-currents anymore and will run in saturation. If you fear that the 1MOhm disturbs your circuit, you have to connect the inputs with lower resistance to GND, not to leave the inputs open.
If the new chip with correct connection of Ref gives you again an output in saturation, I would start with a reduced gain (of maybe 100), so that the output of the amplifier shows meaningfull values. Based on those you can learn about the influence of various error sources (like power supply ripple, parasitic capacitance at Rg, high source resistance, insufficient decoupling of supplies, ...). Like Dirk I think, that in the end you'll need some optimizations of the layout (have a good look at page 21 and the following in the datasheet ).