"When the module detects a signal outside a configured temperature range on a channel, the red LED for that channel lights. Signals outside the configured range include those that indicate open thermocouples. The red LEDs do not light in response to out-of-range signals on channels configured for the –20 to 80 mV range."You can find the cFP-TC-125 Operating Instructions here.
I think you are probably correct, it is probably a broken module. I suggest calling us here at NI to try a couple troubleshooting techniques and if that doesn't work, set you up to return the TC 125.
Reggie Rector ¦ Applications Engineer ¦ National Instruments