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Let's say this:

The user is good
the computer is new

the solution is"a good new computer user" or "a new computer good user"

and if
the computer is good and new?

What is the rule?
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The user is good
the computer is new
a good new computer user = a (good (new computer) user)

if the computer is good and new?
a good new computer user = a (good new computer) user

Some combinations are ambiguous, so they have to be recast if the distinction is very important to your message.

CJ
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As mentioned, wouldn't put everything together here. Just too confusing to interprete at the first scan/read.
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Comments  
You probably would not combine the two thoughts in one sentence. Kepp it simple, talk about the computer or the user in each sentence.

As for just the computer... A good new computer.
 CalifJim's reply was promoted to an answer.
 Marius Hancu's reply was promoted to an answer.
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