Labor power is a commodity.
Investing in labor power by going to college is a form of training in Marx's scheme. So that portion of capital is variable capital, but labor power itself is not capital. Actually, one of the conceptual problems with social capital as compared with human capital is that there is no commodification of it. And in slavery, there is outright human capital in the buying and selling of human beings, although masters tend to limit their investment in the human capital of their slaves for fear that they will either escape or revolt. Taking Jim's point a little further, Marx also noted that capital is not a thing, but a relationship between people regarding things, or the like.