A coworker of mine has observed something odd when the computer is turned off. He is using a PCI-MIO-16E-4 to measure the output of a 4-20mA sensor across a 250 Ohm resistor. He also has a DMM measuring this voltage. When the computer is on, the DMM reading is fine. The DMM reading agrees with the values obtained from a LabVIEW program using the DAQ card. However, when the computer power is turned off (and the DAQ card is still hooked up as to take a reading) the DMM's measurement drops from 3.7 to 3.4 Volts (for example).
It would seem that the card is no longer being a high-impedance device, as voltage measuring equipment should be.