Why DSL? That would not be my choice for a general-purpose family computer. I recommend fixing or replacing the CD and installing something like Ubuntu, Mepis, or PCLOS. Any of the modern mainstream distros is going to have everything you need using the package manager.
It is possible that the CD drive can be salvaged by cleaning it, but I think it would be better in the long run to get a drive that will read and write CDs.
Post the specs on the computer for more specific advice---RAM, HD size, etc.
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