You could try manually installing libqtcore4 126.96.36.199-beta1 if it is available then trying again, seeing if you get another error then trying to resolve that and so on. However looking at your OP it mentions updates for natty which is incorrect, mint 9 is based on ubuntu lucid, so there is something else going on here, perhaps an issue with your repos? If you look at the entries in Software Sources, there should be no mention of anything other than (mint 9) isadora and (ubuntu 10.04) lucid.
[Edit] your original post and add [SOLVED] once your question is resolved.
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