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If you are still using the old computer with avast on it, then just get a new key for the new avast on the new computer. Since it is free, it is the easiest resolution.
If you are no longer using the old computer, then it is OK to use the old key in the new avast on the new computer providing they are the same versions of avast ... 4.8 versus 5.0 ... but you will have to get a new key in about 6 months. So, why not just get a new key now and be done with it for a year?
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