I don't know the 1600cd, but based on what I know of the VS series, the problem will not be hard drive related.
First thing I might look at is the discs I am using - I would try to find a handful of other brands to sample (harder today than it was 5-6 years ago, granted), or maybe go for the brand that is consistently suggested - Taiyo-Yuden - although I have never used them myself and have had great luck with Verbatim off the shelf discs.
I'd consider the cd drive secondly - maybe use a cd/dvd cleaning disc a half dozen times, for instance, or consider finding a replacement drive (whatever that model and make may be will be up to you getting into the machine to identify it and then find a compatible unit, probably)
If that doesn't cut it, then I'd consider whether or not there is a software or other hardware fault.
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uptildawn