I have a Kenmore black glass stovetop range and never use soap on it, but it cleans beautifully.
I use paper towels with hot water to remove most of whatever spilled on it. Then follow that with the commercial glass stove top cleaner (Cook Top Cleaning Cream) bought at the grocery store. I apply the stovetop cleaner and then wet a Scotch Bright (has the blue scratchy side) and polish with that, then wipe clean with paper towels. It always cleans beautifully.
I didn't know about the Windex, but that sounds like a good idea too after you get it cleaned.
I agree with the previous post. If none of this works, call Sears and ask them what to do. Good luck.