If a company is registered for VAT then by law they have to charge VAT at the appropriate rate,whatever they sell, even if it is secondhand.Special arrangements apply to some goods such as second hand cars; but as far as I am aware, if you buy a second hand computer from a registered company, they have to add VAT.
In my experience vat is payable if it (i) has not been paid before, or (ii) has been paid and reclaimed, or (iii)there is exemption. If I buy a PC from a dispersal sale I expect to pay vat because the previous owner likely offset original vat paid. Auctions also have vat on the service provided, as part of the commission. Books are usually exempt but may carry some vat for an enclosed cd, for instance. Offshore firms like 7dayshop may have a limited vat exemption, subject to review. Hope this helps.
I know I have receipts for past used car purchases and these include VAT.
In odd cases the sticker cost of the used car and the part exchange allowance have been changed somewhat from the verbal agreements - I presume this is to gain a little more VAT repayment when claimed back...:-)