I own a 99 Z71 Silverado, just like yours.  I get the Service 4 wheel drive also, I dont get the service engine soon though.  But what I've found searching through the net is its a sensor on the transfer case that goes bad.  Cant remember the exact name but can find it for you!  It's suppose to cost between $35 to $65 depending on your dealers markup.  Its suppose to be the fix.  When it warms up here this spring I'm going to look into it.  If you have push button 4x4 like me mine also is a little touchy about going into 4wheel drive some times, but the more I use it the better it is. 

As for your service engine soon light, it could really be anything, the best thing is take it in and have them scan your computer for codes, and see what comes up.  usually about $35 to $75 charge for that, once again depending on where you go! 

Good Luck

USUALLY YOU CAN BUY A CODE SCANNER FOR THE COST OF A SERVICE VISIT OR EVEN LESS. THEN YOU CAN CHECK YOUR OWN CODES AND YOU WILL HAVE IT AROUND FOR FUTURE USE. THE MAJORITY OF THE TIME THE SERVICE ENGINE LIGHT IS TRIGGERED BY A BAD EGR VALVE OR OXYGEN SENSOR. THEY ARE BOTH PRETTY EASY TO CHANGE

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ORIGINAL: Reggies1956

Ok. It started today. I have a "service engine soon" light on, on my 2002 Blazer. I called the Chevy dealership= $89.00 for a test to determine the problem... I then took it to Autozone for the free test, and was told that it appears to be the thermostat or a temp senser. I had a radiator flush with new antifreeze put in about 3 months ago, and since then I've noticed the temp hand is lower at about the 1/4 mark. I had to travel about 40 miles early this morning in the coolest temp of this season. It was about 30 degrees when I started. Then that light popped on. I'm thinking it might be the thermostat maybe hung up in the open position allowing cooler water temps. Should I change the thermostat first ? I was told it might take 20-30 miles of driving afterward before the service engine light would go off. Does this sound correct ?