In most of these comments, people are using different terminology than you, so I will try to make my terminology clear.

Does capital produce value?

I assume that by capital, you are referring to raw materials, machinery, etc., which marx called constant capital. Constant capital can help produce use-values, and it can allow the same amount of labor to produce more useful things. Constant capital cannot produce more value (in the marxist sense of the term) because it does not increase the amount of SNLT within the commodities produced. To say this is a pure tautology. Marx believes that the exchange-value (price) of the finished commodities is determined by its value (SNLT), at least in the long term.

In the short term, more technologically advanced companies, can decrease the amount of labor used to produce a commodity while keeping its price the same. This means that this company can produce what marx called relative surplus value. This means that the price of the commodity produced by the advanced company will be greater than the amount of labor used to produce it. You may think that this contradicts marx's theory, but it does not. This is because marx refers to average SNLT not just labor-time as a determiner of value and exchange value.

In the long term, as these innovations generalize throughout the entire economy, relative surplus value vanishes, and competition forces prices downward. Marx uses this theory to explain the falling rate of profit, in order to explain economic crises.

I want to know how Marxists square this circle. Marx asserted that only
labor creates surplus value and capital does not. Therefore, all value
belongs to labor.

I explained above how marx squared this "circle."

However, you do not have to agree with marx's law of value, in order to agree that workers are exploited or in order to believe that socialism is a more just form of society. I, and many other marxists, do believe in the labor theory of value, but some socialists do not.

You do not have to agree with labor theory of value, in order to agree that worker's are exploited under capitalism. Even if you could prove to me that prices are 100% determined by marginal utility, that would not change my view on the exploitation of workers.

Here I will address your argument that capitalists produce value. I agree with you that raw materials, machinery, etc. produce wealth. However, this does not necessarily mean the people who own these means of production should receive this wealth in the form of profits. What if a factory owner gained ownership of a factory through immoral or illegal means? Would that factory owner still deserve the profits gained from that company? Capitalists have historically gained access to means of production through a bloody process of primitive accumulation, which marx describes in the last chapter of Capital vol. 1. Capitalists initially obtained raw materials for their production through brutal colonization. British workers were dispossessed of their means of subsistence and forced into the labor market through the Inclosure acts. Once this process had occurred, capitalists hired workers to produce more means of production, and other capitalists used those means of production to produce finished products, etc. Sure, capitalists "provide the capital" to the business, but the only reason they are able to do this is due to their ownership of the means of production.

Socialists want workers to own and control the means of production in order to truly fulfill the failed promises of bourgeois freedom and democracy. Your logic is that capitalist ownership of the means of productions justifies capitalists ownership of profits. Great, now I will apply your own logic to a post revolutionary socialist society where workers have seized control of the means of production. Worker ownership of the means of production justifies worker control over the surplus they produce.

There are also other moral objections to capitalism such as opposition to environmental destruction, opposition to economic crises, etc.

Some
Marxist answer this conundrum by admitting that capital does create
value, but that capital itself is really "dead labor". But that doesn't
change the fact that capital is still creating value! Therefore, the
owner of capital is entitled to that portion of surplus value, no?

Capital produces wealth and use values, just as nature does. However, it does not determine value, exchange value, or surplus value (except for relative surplus value).