No. T-Cut would not come up good. I've had incredible results with a product called Goo-Off 2 which you'll find in the paint preperation section in paint shops. This will clean it up a treat.
If you have scratches, then head to an automotive store and pick up some Mother's Scratch Remover - or an equivalent. It is expensive though.
Really bad scratches might need to be sanded. Take the case off, use the finest grit wet 'n' dry sandpaper you can get (buy a couple of sheets from an automotive paintshop). Dip the sandpaper in water and sand VERY gently until the scratch starts to disappear - you won't be able to eliminate it completely, just make it small enough for scratch-remover to be able to work. Use a buffing cloth to buff it down smooth and then a bit of scratch remover to finish the job.