Not all skipping is caused by the new chain on old cassette phenomenon. While it's possible, I wouldn't have have expected that a cassette could wear to where a new chain skips in so few miles.
Also the new/old issue usually affects only the one or two most used sprockets, and/or the smaller ones.
So before giving up, I'd do some due diligence and check for things like RD trim.
OTOH - if you saved the old chain it's the best clue about the current issue. If it's stretched only 1/2% or so, then odds favor the cassette being OK. More than 1% odds are against the cassette, and in between then anybody's guess.
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FB
Chain-L site
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Last edited by FBinNY; 10-05-15 at 04:52 AM.