So if there is no difference in bargaining power, the only thing left would seem to be subjective value.

Sure, except there is always a difference in bargaining power. The capital owner always has a greater ability to subsist without needing the worker than the worker does without employment under the capital owner. Even 18th-century political economists knew this.

Computer programs use an order of operations that we give them based on how quickly we want certain things done(value).

Operating systems, which is what I was referring to, use priority queues, where the most critical operations occur first.

This is not like the free market, where an operation makes a bid of how much it's willing to give the operating system in order to get computation time; this is basic communism, in which the operating system gives according to its abilities to each operation what it needs.

Why would they create a market, when they exist in and their entire ability to purchase things comes from a market?

Indeed, why, if markets are what is responsible for allocating resources efficiently, would they need to create new disciplines of applied science in order to allocate resources efficiently? Why would the military use a hierarchical command structure to allocate its resources most efficiently, rather than letting the free market take care of it?
Why would Wal-mart centrally plan the distribution of its stores, set up stores that it knows will not succeed, and offer loss leaders, if central planning is futile and prices are the only thing that is needed to rationally allocate resources?

I'm really trying to understand this new economy model because I would like to believe in it. So I would really appreciate some more well thought out examples if you really care to convince me or other people.

You can take a look at my website which contains some more thoughtful explanation than I am capable of providing here. In the context of rational allocation, I have produced the priority theory of value, which can be succintly stated as: "Value is based on what is most critical to us".

Other than that, I would really advise you to take a more critical look at the claims of proprietarians: If the free market allocates goods efficiently, why have we consistently depleted our stocks of resources, destroyed the environment, and produced waste more than any other product in the last century? If the free market is really voluntary, why do "free markets" consistently have large police states and clear class divisions? If the free market really reflects what we value, why does it consistently value property over people, wealth over need? Why are there so many actions we want to take which are not "economically viable"? Most of the claims of the efficiency, efficacy, and beneficence of the market do not hold up to what we can observe.