I wrote a poem "Root of Karma" while contemplating this question that has probably been asked a million times so far in the history of the known universe. I have been a questioner all my life. I always question to understand... I know there are cases where the answer is unknown to humans. But the answer is there... only Bhagavan knows it.
May be the details of the root of karma are not relevant for me and hence the information is not needed for me. I also have accepted certain things are indeterminate in the field of mathematics... so the concept of something being indeterminate is not unacceptable for me. Infact, I wrote something on this in my blogsite a few weeks ago when I had resigned to not seek answers to some of these questions: http://lokakshemam.blogspot.com/2007/05/irrational.html
But this question keeps hankering me... like a nagging doubt, it comes back to me. It is very wierd as to how when we try to go deep into the roots of a few simple things we take for granted... we get flabbergasted. It is due to daya on us that many Acharyas (teachers) have prescribed not to delve too deep into this topic. I will try but my swabhavam is one of contemplation and thinking... even though faith comes to mnaturally, I am also a deep thinker! I also have found that some times questions that I have, get answered from unexpected sources.
I think the root of karma is an indeterminate for my mind as much as the square root of 2 is indeterminate to the fullest extreme to humans (as it has a non terminating, non recurring decimal). And true enough someone like Brahman or Bhagavan who is not limited by the constraint of time might be able to tell exactly what the 1 millionth millionth trillionth decimal place on it without any problems... I guess my brain is not wired to do that.
My humble conclusion is that Karma is anaadi in the sense that the root is too deep for me to compute... but the one that comprehends all just knows the root of all!