I have tiny roots, from I don't know where, that are so thick I cannot get a shovel into the ground. These are not roots like from a tree. They are very small and dense.
What is growing in that area? You need to see if you can figure out what plant these roots might be coming from. You might also want to contact your local extension office (found under government in the phone book). They can better help you determine where the roots are coming from and how to deal with them.