I am not sure if this is the answer, maybe C4C5 specialist can contribute as he knows more than I ever will know. You could alway PM him if he misses this post. The TP sensors operate on a battery in each valve stem, and since your vette is a 1997, the batteries may have all expired at once since they are good for about 6 to 8 years, sometimes longer, sometimes shorter. The TPS system works whether the car is stationary or moving. The difference is that while stationary, the sensors transmit a signal every 60 minutes because the internal roll switches are open, while in the moving mode, the sensors transmit every 60 seconds because the centrifugal force closes the internal roll switches. The data transmitted for each tire is for sensor presence (LF,RF,RR, LR), sensor mode (stationary or moving), and the tire pressure. Assuming that the batteries are still powering the sensors, you should get a reading on the DIC. If the DIC indicates that there is a problem with the sensor system, it could mean exhausted batteries, bad receiver (RCDLR), or some other problem. Since the batteries are not replaceable, you must purchase new sensors for each wheel, as they are wheel specific. Unfortunately for you, the pre 2002 sensors are more expensive than the 2002 - 2005.
The sensors are reset with the use of an external magnet that you place next to the stem; the magnet pulls the internal roll switch up and then lets it retract inside the valve system. Try to reset the sensors first to see if this is the problem.
Hopefully someone else can contribute more to your problem.
Barrett