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