I am assuming that when you connect the ADC-16 to the three PCs you are using the same serial cable. If you are not then use the one which works this will eliminate the possibility of a faulty cable.
Check the serial port input/output settings: 03F8 - 03FF.
Check the voltage being supplied to the ADC-16 from the PC's, for those which are not communicating.
Connect the ADC-16 to the PC in the usual way and start Picolog, once you get the error message test the following:
Pin 4 >7
Pin 5 GND
Pin 7 <-7
This can be tested by unpluging the cable from the ADC-16 and using a multimeter on the relevent pins on the cable. The ADC-16 could still work if you get voltages around the ±6.5 volt mark any lower voltages would stop the ADC-16 from working.