Welcome to the NI Discussion Forums! It looks like you are having some trouble measuring your full bridge strain gauge with your SG04. You were able to get your strain gauge to read properly with the SG02.
The SG02 is used for quarter bridge strain gauges since it contains all of the completion resistors needed to perform a quarter bridge measurement. The SG04 does not contain any completion resistors since it is used for full bridge strain connections. It does contain the necessary components to null your strain gauge. If you check out page 18 of the SG04 manual it shows you how to see if your strain gauge has a high offset error. It looks like that since your signal is stuck at 68m with no load then you most likely have an offset in your measurement. This offset can be calibrated out in the hardware. Follow the steps on page 18 to ensure that you are calibrating out the strain offset. After that perform the next set of steps to calibrate out any gain error on your measurement so you can have the most accurate strain measurement possible. Also, the m in 68m stands for milli or 10^-3. Since strain has no units, then 68m is 68 millistrain that is commonly represented with a ε. Post back if you have questions.
Have you tried creating a custom voltage with excitation task to see what voltage value you are reading? This type of task doesn’t scale the voltage read into strain, but instead leaves the measurement as volts. This will give you a pretty good indication of the voltage that is being output by the gauge. Make sure this seems reasonable from the task. You can also connect a battery to measurement terminals of the SG04 during this type of task to ensure that you are measuring the voltage correctly. Also, hook a DMM up to the excitation pins of the device when the task is running to see if the excitation is the value you expect. Make sure that the excitation is also set to the specifications of the gauge you are using. If it reads a reasonable voltage (from the battery and the gauge) and the excitation is correct then your hardware is working fine. Make sure to select an input range in volts for the custom voltage task and in strain for the strain task. It could be that your range is not set correctly.