The shipping (which I presume you are referring to when you say "flat carriage rate") should not be included in the product price. So, excluding any changes in very recent software releases, that should not be a problem.
So, depending on which version you are working with, your problem should be in specials, salemaker (if present), taxes (if using display prices with taxes and the problem affects all products) or product group pricing.
Further, you MAY have a problem with a template file or a code bug somewhere. This I base on the variance in pricing you mentioned. Ideally a template should be using the price formatter class everywhere a price is displayed, using raw price methods where custom display is needed. This seems to be rare in actual practice...
Start by checking the available discounting components to see if someone has set a 10 euro discount on that product. Then get back to us with the details soundzgood2 asked about, plus whether the problem occurs when logged in to begin with or when logging in during the checkout process....
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