2005 TrailBlazer 4 wheel (Dtc light) light came on. We have changed differential fluid. The switch on dash board will not change in addition we hear inside the car rumble. Towards front . No code comes up on computer. When it rains the light will go out ? Is driving and turning fine.

First you need to have EBCM - electronic brake control module check for DTC'S - diagnostic trouble code's . If the light is on there is a code stored . I think most part stores can do this and for free . After you find out what code is stored , looking up that code in service repair information for diagnostic trouble shooting chart would be next step . There are a few codes too.
DTC C0035 or C0040
DTC C0045 or C0050
DTC C0110
DTC C0131
DTC C0161
DTC C0186
DTC C0196
DTC C0201
DTC C0240
DTC C0241 or P0856
DTC C0244 or P1689
DTC C0245
DTC C0283
DTC C0287
DTC C0290 or C0292
DTC C0455
DTC C0550
DTC C0558

Find the code do the diagnostic's , fix the problem , wiring issue's , a sensor , bad module ,what ever it is . The light will go out then . Here is a sample of code discription .
• DTC C0035 Left Front Wheel Speed Sensor Circuit
• DTC C0040 Right Front Wheel Speed Sensor Circuit

There are actuators on the front axle and the transfer case, check them both.

always put in neutral before switching in or out of 4 wheel drive unless vehicle is equipped with on the go shifting

The fluid should be changed at the 100K mark. The front and rear differential fluids should also be changed at that mileage. The transfer case fluid needs to be changed every 50K miles and only use GM Autotrak II gear oil.

First of all, the noise is not coming from the rear. The noise is only happening in 4WD mode, that involves the transfer case and front differential.
When was the last time the transfer case fluid change, it is recommended that it be changed every 50K miles. It is possible that you have transfer case issues. It is not recommended to operate the drive system in Auto mode constantly, this will wear out the internal clutches.
If the road surface does not warrant 4 wheel drive, keep the selector in 2WD.

When you switch from 2HI to 4HI, you should hear two distinctive sounds from under the truck, one is the transfer case actuator and the other is the front differential actuator. If you hear both and you still do not have power going to the front wheels, then there is a problem with the front disconnect assembly.

What do the lights on the 4x4 selector switch do when you switch to A4WD or $HI or 4LO positions? Do they blink and revert to previous selection? Has the Transfer Case fluid been changed at 50K intervals?
There are actuators on the Transfer Case and Front Differential that control the application of power to the front wheels. These actuators are controlled by the TCCM (Transfer Case Control Module). It takes a qualified 4 wheel drive technician to diagnose these systems.

Was the transfer case fluid changed every 50K miles? This very important on these trucks. The Transfer Case Control Module (TCCM) could be at fault, especially since you have no lights on the selector switch. Is the Service 4x4 light on? When you switch from 2H to any of the 4 wheel drive selections, do you hear any actuator noises coming from under the truck?

usually the actuator will still make the light still come on if its bad I would check the actuator

the switch on the dash needs to be replaced.