Is it possible to reconstitute a labor theory of value? I am not an economist, so highly technical answers may escape me. I know that since Jevons, Marshall, and the "marginal revolution" the classical labor theory of value has been largely abandoned. And clearly, some concept of utility must inform pricing at some level.

But is there any inherent reason why a labor-based system of value and pricing adequate to a modern market economy cannot work? Have any been proposed? What would be the consequences or shortcomings of such a system?
It would be helpful if your question were a little more honed in. This is a very broad set of questions about an entire theory, but a few thoughts that come to mind.

The labor-theory of value naturally predicts that profits will be higher in labor-intensive industries, as opposed to capital-intensive industries, and that's simply not what we see in the data. A firm needs a good balance between both capital and labor. Also note that in developing countries, labor is plentiful compared to capital, so wages are lower and capital is expensive. As welfare and the capital stock increases, labor becomes more sparse since there is more to do with leisure, so wages rise and the price of capital falls (we are better at producing capital.) So in some vague way, the price of a good depends more and more on labor as the development of a country increases, but not because of the intrinsic value of labor, but because of the marginal cost of labor for firms that increases.

When you ask,


  But is there any inherent reason why a labor-based system of value and pricing adequate to a modern market economy cannot work?


you assume that there is a system like this that is "adequate". It's not that labor has no place in production or determining the price of a good, but we have models that are better because they realize there's more than just labor that goes into production. Labor does not exist in a vacuum. Today we take into account both the value of labor as well as the value of capital, amongst other factors of production. Why would we want a model that ignores these things for the sake of saying the price of something should only depend on the amount of labor put into it.

A final note: in industries where worker labor is overwhelmingly the major part of production, the wages paid out are essentially the value of effort put into the product. The worker maximizes

See the second part of my answer to this question to see the mathematical set-up for that result.