The service brake system light comes on and the 4 wheel drive selector switch works sometimes and sometimes doesnt

Can't be to sure with yours. It maybe the switch. On my 2002, I found I had a Transfer Case Control Module issue. Shopped around and found one on Amazon for half the price the local box stores wanted. I would Google this before starting to buy a bunch of parts.

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4WD Transfer Case Position Sensor/Selector ... - RepairPal

repairpal.com > Problems > Chevrolet > Tahoe
Service 4WD Message May be Displayed on Chevrolet Tahoe. The 4WD transfer .... I had a similar problem with 4 wheel drive selector switch. When I select 4 ...

4WD Transfer Case Position Sensor/Selector ... - RepairPal

repairpal.com > Problems > Chevrolet > Suburban 1500
Service 4WD Message May be Displayed on Chevrolet Suburban 1500 ... When in 4 wheel , it will not in engage sometimes and message comes on to service 4 wheeldrive. ... I replaced the 4wd transfer switch in 2007 and now again it is not working, this would be the ... 2008 Chevrolet Suburban 1500- 4WD156,000Visitor.

Chevrolet Tahoe Repair: Problems, Cost and Maintenance

repairpal.com > Cars > Chevrolet
Having problems with your Chevrolet Tahoe? Learn about common Chevrolet Tahoe problems, recalls and typical maintenance and repair costs. ... ABS Front WheelSpeed Sensors May Fail. Chevrolet Tahoe ... 2008 Chevrolet Tahoe.

ON LEVEL GROUND
With the transmission selector in "park", start the motor.
With your foot on the brake pedal (steady-constant pressure), move the transmission selector gear to neutral- then turn the 4 X 4 selector knob to 4-wheel drive high. Wait for the 4 X 4 engagement.
Once it is in 4-wheel drive high, with the transmission selector still in neutral, quickly pump the brake peddle twice, keeping you foot on the brake pedal on the second pump, turn the 4 X 4 selector knob from high range to low range. The transfer case should then change from 4-wheel drive high to low.
Electronics being what they are, you sometimes have to repeat the process. You may even have to inch forward or backward.
[I have an '01 Excursion and an '05 F250 with 4 X 4 on the fly...I miss my '97 F250 with the manual 4 X 4 shift on-the-floor!]
Anyway, check the fuse panel for any blown fuses.
Double check to make sure that the problem is not just blown 4 X 4 lights on the instrument cluster. With the nob turned to 4-wheel drive, have a second person- a spotter, check to see if the drive shaft to the transfer case is moving. If it isn't, you have to delve into the troubleshooting process.
Check the solenoids, vacuum hoses, vacuum actuator, and transmission range sensor on the transfer case. .

You need to have your foot on the brake, put the Trans in Neutral, and then shift the Selector to 4 Wheel low. If this does not work you need to check the wire at the transmission for Voltage changes. Each position on the selector has a Resistor and they use 1 Servo to make the gear changes. You need to see if the Selector has different Voltages in each position. If it does, then the Servo is not responding.

But do not forget the Interlock of the brake pedal for the gears to change. Also check for light at the Selector switch. If the lightbulb is burned out you will sometimes throw off resistance and wind up missing functions.

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?

The  actuator on the front diff or transfer case is stuck or bad. This will send a signal back and turn on the service light. In 2003 I believe the actuator is on the front differential.  

Do you have the push button selector switches or the handle on the floor?

push button 4-wheel drive??? If so maybe the transfer case motor? look on back of transfer case for something that looks like a window motor.... have a friend, while on level surface in nuetral with brake depressed, try pushing 2-wheel button while you lightly tap on side of window motor with light weight hammer or wrench. If this doesnt work then motor may be bad.

i had same problem for almost 6 weeks . I just replaced my batty and it fixed the problem compleatly

change the selector switch first it is by far the cheapest