Ah, I love the smell of plastic-talk in the morning (and by morning I mean late afternoon). It's a passion of mine.
Toothpaste is wonderful if you are trying to remove scratches from plastic (it is an old Jedi mind trick, and my Jedi mind trick I mean model-kit technique), but that really says nothing about if a player can still read it. Toothpaste is essentially very fine sandpaper (only, you know, sans the paper). Using it just buffs the entire surface down to the same level as the scratch and smoothes everything else, but if the scratch wasn't the problem in the first place... And you are basically adding countless micro scratches to the disc anywho
Boiling CDs... never heard of that, but if I had to guess I'd say that would work nicely at removing some dirt and oil. Just be sure to not heat a CD to around 150 Celsius (glass transition state for polycarbonate, which is the usual makeup of CDs, if I am recalling correctly). Heck, just stay away from anything above 100 really (not usually a problem in
water, admittedly).
... actually, if you have a disc that is just absolutely ruined by a crack with no hope of return, I suppose you could take a heat gun to it (actually, a non-convection oven might be better, since in a glass transition state the air itself might dent the plastic in undesirable ways). Heating it to the glass transition state might smooth it out enough fix the problem, but that is probably just the crazy in me talking.
Suppose one could also take a trip down to a local plastic shop (
or browse online) and see if they sell anything for repairing cracks in polycarbonate too.
Personally, I find that a simple glass-cleaner rag thingy that we near/far-sighted type use for our eye-wear works wonders on CDs. They don't scratch and seem to suck up oil and dirt.
Curiously, I have been told that damage to the back of the CD is actually more likely to permanently ruin the CD than damage to the front. Supposedly the back is thinner so humidity can various chemicals can get in easier through undetected cracks.