My 97 cruise control didn't work. If you have a service manual you can figure out how to troubleshoot it. In my case, the LED in the steering wheel always came on. Initially I found a vacuum leak where the vacuum hose connects under the battery holder; however that didn't fix the problem. I eventually found the problem was a hole in the side of the control servo itself. Once I replace the servo and the cable everything worked great.
Since your LED doesn't come on, I'd first check that power is getting to the switch control module.
I'd also check the stop lamp switch on the brake. The cruise control system is routed through contacts 3 and 4 on the stop lamp switch (pin 1 is the furthest from the plunger). These have been known to go bad but I'm not sure what the indications are if it fails. After looking at the manual's wiring diagrams, it looks as if the contacts between 3 and 4 on the stoplight switch are normally connected; however, the troubleshooting procedure in the brake section states they are only connected when the brake is pressed. So I really can't tell you what you should see at that point(maybe someone else on the register can) . If the connection between these two contacts had failed, then it appears the LED may never come on.
I'd leave checking the switch control module until last because it seems the most complicated. Apparently the switch control module has been known to fail in the past. According to the service manual, there are two ways to check the system. If you have a DRB scan tool and the other is to use a volt/ohm meter. The DRB process is pretty long so I won't go into it all here but the codes from MIL check are as follows:
MIL code - 12 - Battery input to PCM disconnect within last 40 key-on cycles
MIL code - 15 - No vehicle sensor signal detected during road conditions
or
MIL code - 15 - Output shaft less then 60 rpm with vehicle speed above 15mph
MIL code - 34 - open or shorted condition at speed control vacuum or vent solenoid circuits
or
MIL code - 34 - speed control switch input below minimum acceptable voltage
or
MIL code - 34 - speed control switch input above maximum acceptable voltage
MIL code - 56 - completion of fault code display on check engine lamp
MIL code - 77 - No power at speed control circuit
If you use a volt/ohm meter, you need to be careful when doing the check because you have to take the steering wheel apart.
YOU HAVE TO DISCONNECT AND ISOLATE THE BATTERY(S) NEGATIVE GROUND AND WAIT FOR AT LEAST TWO MINUTES OR ELSE THE AIR BAG COULD DEPLOY.
Capitalized the previous sentence since it is all caps and bolded in the service manual.
After you remove the speed control switch module from the steering wheel, you can check the switch continuity. Looking at the back you will see three pins. If you label the pins from left to right 1, 2 , and 3, you should get the following measurements:
No switches depressed - resistance between 2 and 3 should be 0
ON switch pressed - resistance between 2 and 3 should be 909 ohms +/- 9 ohms
Resume/accel pressed - resistance between 2 and 3 should be 15400 ohms +/-154 ohms
Set/Coast pressed - resistance between 2 and 3 should be 6650 ohms +/- 66 ohms