Sure, it's got some market value in general, but how much is it worth accumulated in a single place?

The same as its market value in general.

Large parts of the reserve cannot be spent, used, distributed in any significant way. So how much that gold backing part of the system really worth?

I believe you're referring to the U.S. gold reserve at Fort Knox?

That reserve is worth its value to the owners (U.S. citizens) as an asset. For example, your family might have an expensive set of solid gold and silver cutlery, continually handed down. It's never actually used, and is kept stored away. However, if one generation of your family loses absolutely everything, at least the gold and silver cutlery would be one valuable asset your family could cash in on.

Not saying that it's reasonable to suspect otherwise, but at the moment it seems we use money, because the government tells us it's OK to do so and what the value is. Is it really the gold backing anything in that case?

President Nixon removed the U.S. dollar convertibility into gold in 1971. It is not gold backing that currently gives the dollar its value.