I am measuring strain from a full bridge using a 5B38 module (3.33 V excitation), a 5B08 backplane and a PCI-6024E board. The board is configured in NRSE mode, DC coupling. The problem is that, when no load is applied to the strain gages, the board is measuring arround 3.33 V (approx. the excitation voltage).
It sounds to me as though there is something in the physical connections of the strain gauge to the module. I would verify the connections with the picture that I am attaching to this post. Also, I would ensure that there are no bridge connections left-over from old half or quarter bridges that are bridging the module terminals. Also, I would verify that the strain gage itself is still good. You could try a different strain gage or verify the resistors are still good. Another thing to verify that the ohm rating of the strain gage matches up with the range for the module.