I'd start with good old fashioned soap and water - the same soap you use to wash your dishes. Put a couple of old towels on the floor and use a saturated rag to wash the surface. It would be really good to have a window squeegee to wipe of the surface. Buff out any remaining streaks with a paper towel.

Let's see where that gets you.

I use plain old Windex to clean my stainless steel. I spray it on fairly heavily and then wipe it dry, with the grain, using an old towel. They I lightly spray another towel with Lemon Pledge and run that with the grain to shine it. I've tried just about every stainless cleaner on the market and this method works better and is far cheaper.