Perhaps the most important element which determines the value of an individual machine is the company by which it was manufactured. Many machines may have different company names, yet be otherwise identical. This is usually due to sale in a differnt country to that of manufacture. All machines which entered mainstream production, and have not been extensively modivied, will include a company name or logo in a prominent position. Any unmarked machine is very unlikely to have been mass produced, and therefore there is no precedant by which to determine a fair price. However, it is to be noted that these machines are immensely rare.
This determines the rarity of the calculator. A rarer machine will usually command a higher price, although one must take into account the fact that older or less robust models are less likely to have survived.
On most calculators this has very little effect, other than to help in identifying the model. There are naturally a fer exceptions. A serial number which can prove the machine to very close to the start or end of the production run may increase the price. Furthermore, on a Curta (the market for which is for the most part seperate from that for all other calculators), more 'interesting' serial numbers may increase the price, such as prime, semi-prime, twin prime or palindromic numbers.
The effect of a working mechanism on the price is harder to define. This is partly because many sellers will state this on the listing (either because they do not know how to test the machine - see my instuctions at the bottom of this page, or because they do not want to admit that it is broken). Many collectors, including myself, restore the calculators themselves, and so the functionality is of less importance. Obviously, if parts are missing, the machine will not function. It is also more likely, although not guaranteed, to be working if the registers all display 0s, and it is cosmetically good.
This does not affect the value particularly in and of itself, however a cosmeticlly poor calculator most often is syhmptomatic of neglect, which may well entail rust, stuck or broken parts, and a long time since the most recent oiling.
Concise instructions to test the functionality of a calculator.