It appears to me something has been nibbling on those roots, likely favoring the tender growing tips. This stunts growth and sometimes kills the plant. Often plants can survive and grow to produce a crop, but usually reduced in size and vigor.
Unfortunately, it would be hard to say what the culprit is. It could be root maggots, symphylans, wireworms. I would suspect some sort of root maggot if I had to hazard a guess, even though you couldn't find any. There are several species that will feed on cabbage family roots, and I don't think Bt will stop them.

Neither clubroot nor Rhizoctonia.

Likely to be cabbage maggot.

Found a good image of damage on canola root at
http://www.canola-council.org/gallery/855/pests_insects.aspx?photo=12

So I guess you'll be studying up what to do next year to avoid. For one, you need to plant in a different place.

Most likely, local agricultural/garden people in your region have info for you. In the meantime, take a look at what the University of California says at
http://www.ipm.ucdavis.edu/PMG/r108300111.html

Good luck.

Here is a link that might be useful: damage on canola root

cabbage root maggot?

Cabbage maggot is common in the Midwest. The moths are white, they are attracted to cabbage family plants including Cauliflower, they lay eggs at the base of the plants and the maggots eat the roots.

I think the root maggot is fly larvae not a moths. The moth larvae eat the leaves. Sounds like the evil duo. I have lots of trouble with root maggots in my early barssicas. Tom

Thanks for all the responses. I thought about root maggots as well but thought you can always see them. Is it possible that they are not visible at all? Is there anything I can do to make sure they don't start eating my red cabbage or radishes (since they are in the same family)?

You can use a lightweight row cover when you transplant out