More on the topic of removing CD scratches from Campbell R. in New Zealand:
"Further to the bloke from Chile (inSync TTOTD 6/19/97) using Brasso on CD’s. For really bad scratches, I have found wet and dry sandpaper really good, starting with 1200 grit and working up to 2000 grit and then finally the afore mentioned Brasso to finish! Two things to keep in mind are: 1. Make sure you don’t get any grit under the CD as you are polishing, because the side with the writing on it is extremely close to the actual CD info and if you scratch THAT side, it’s a throwaway! 2. Make sure it’s not a more viable option to buy a new jolly CD!"
Ed. Note – Taking sandpaper (of any grit) to a CD is fairly extreme behavior (or if you prefer, behaviour); but if the disc in question is irreplaceable and seemingly irrecoverably damaged, you might give this tip a try!