I don't think Marxist economics per se will shed much light on the economics of the current crisis. Marx did not, I think, intend to create a complete and detailed analysis of how capitalism works, nor have his successors pursued such a project. OTOH, one could very well say that Keynes was a capitalist economist heavily influenced by Marx, and Keynesian economics is itself Marxism applied to capitalism. Keynes didn't get it all right (neither did Darwin, Einstein or Heisenberg), but he got enough right to be to economics what Darwin et al. were to science.
The fundamental issue is not really economic. Keynes described, and we (at least those of us who read him) already understand the current crisis in broad terms: it's an almost paradigmatic case of conflation of risk and uncertainty, and the massive transfer of effective demand from the working and professional-managerial middle classes to the capitalist class. We have massive unemployment because industry can't easily shift employment from production of mass-market commodities to ultra-luxury commodities for the tiny capitalist minority, and also because in the face of uncertainty, members of the capitalist class are hoarding their wealth to compete in the now sharper struggle for power within the capitalist class.
The deeper issues are social and political.
I keep seeing liberal and progressive economics blogs give us laundry lists of things we "should" do, all of which make perfect sense according to Keynesian economics. It seems not just correct but obviously correct that these "shoulds" are required if capitalism is to retain what little positive social and political morality it ever had. We knew six decades ago what we should do, we actually did many of those things, and they were successful. Given that Keynes is not just correct but obviously correct, and given that the entire capitalist west successfully ran their economics (more or less) along Keynesian lines for almost thirty years, we must ask: why did the capitalist class abandon Keynesian demand-side economics for classical supply-side economics? If we don't understand at a deep level why we abandoned Keynesian capitalism, we don't have a hope of restoring it.
I see Marx's chief contribution as the understanding that social change is not an ideal process, a process of coming up with new and better ideas, ideas that are adopted and rejected on their abstract merits. Social change is rather a material process, an interaction between physical, material forces (and the thoughts that people actually think are most definitely physical, material properties of our material brains). Marx was, perhaps unfortunately, more a philosopher than a scientist, and his conception of historical materialism is primitive, and substantially incorrect in places. (I can't remember the specifics, but I've seen interpretations that communism is a "science" in the sense of a systematic philosophy, not an empirical discipline conducted according to the scientific method.) Still, if even the charlatan Freud deserves credit for at least persuading the world that psychology could be a science (and he does), the more intellectually honest Marx deserves credit for saying that social development is a material process and can be studied scientifically.
Marx's contributions to historical materialism have been developed — perhaps again unfortunately — mostly by humanities academics, politicians and revolutionaries, rather than scientists. Not to knock any of these endeavors, or those who pursue them, but philosophy is not science, and revolution is the bastard child of desperation and expediency: necessary in some cases, but hardly conducive to the rigorous and dispassionate self-scrutiny required for effective scientific investigation.
Still, one can draw some straightforward conclusions directly from Marx. Most obviously, no abstract quality of an idea can ever act directly as a causal force for that idea's adoption (or rejection) in society. For an idea to be adopted socially, a group of people must actively understand and believe the adoption of their idea is in their interest (and it doesn't hurt if the idea actually is in their material interest), and they must organize and act to implement that idea.
You can tell me we "should" do this, and we "ought" to do that, and I can even rationally understand that you're correct, but unless you tell me in whose interest the idea is, and how they're going to organize and act to implement the idea, you're just building castles in the clouds. (It should be pretty clear right now that simply voting for the Democratic party is not a plan for actually restoring Keynesian capitalism or its underlying moral values.)
Looking more deeply, we can see deep parallels between "Marxian" dialectical materialism and Darwinian biological evolution. The mechanisms are very different, of course (and Darwin himself still counts as a genius even though he did not discover the most important mechanisms of biological selection). Indeed one can clearly see that biological evolution is a material process. More importantly it is essentially a dialectic between the "contradictory" forces of heritable variation and natural selection.
We can extend that paradigm to social and political evolution. First, social selection seems to operate not at a scientific level, but at a moral level. Classical economics is only partly a scientific attempt to understand economic behavior; it is as well (as Keynes himself noted) a theology to justify a set of moral values underlying Randian laissez faire capitalism. (I think we cannot overestimate the impact of Atlas Shrugged as a "rallying point" for those who shared Rand's moral values.) Second, both natural and artificial selection are negative processes: ideas no less than genes are selected not for but against. Therefore any idea available to variation that is not selected against will persist and spread. And therefore we can conclude that — whatever the mechanisms of variation, heritability and selection — Randian moral values were not selected against. Furthermore, some of the moral values that found expression in the particular Western implementation (half-assed as it might be) of Keynesian economics were selected against.
We do not need more "good ideas". Well, we always need good ideas, but we already have a whole store of good ideas that are not being implemented, and coming up with even more new and better ideas is not our immediate task of the highest priority. What is more important is to apply both our understanding and our will to intentionally selecting ideas. And since selection is an essentially negative process, we must select against "bad" ideas, ideas that do not further our interests, especially our material, economic interests. Right now, the selection pressure of liberals and progressives is serving at best only to slow the adoption of "bad"* Randian moral values.
*Ideas that work against my own material interests and those of (I hope) most of my readers.
The "problem" is that if the people actually develop the will and power to perform this selection, if they develop this will more than intermittently to temporarily and minimally alter society only in conditions of incredible hardship, then they'll go all the way to revolution and eliminate the privilege of the capitalist class. There's no middle ground: if they do not develop this will more than intermittently, we will continue to cycle between prosperity and catastrophe.
Keynes has adequately explained the economics of the current crisis. But only Marx shows us the political and social way out.