Solution
The NI 9234 is capable of measuring the quasi-static force. This measurement can be made by configuring the device into DC mode.
To do this, you must configure the Analog Inputs coupling property to
DC coupling.In AC mode static voltages will be filtered out and the NI 9234 will indeed only measure changing voltages. In DC mode, the voltage goes directly to the AD converter and you can detect also static voltages.
The piezo electric load cell can only measure dynamic changes, as any charge will leak through the lowest resistance path and the signal will go to zero after a while.