Older homes drain tile consists of 12" sections of clay pipe spaced about a half inch apart covered in pea gravel. Once the roots from trees and shrubs find them they don't have a prayer. I just went through this with my house this spring. Thankfully it was only the north end and the tile coming from the front of the house was only about a 1/4 filled with roots and was flowing fine.
The fix is to dig it up and lay corrugated pipe with the filter sock. If the basement isn't ruined, beat them down on price and prepare to be able to sell a house with a dry basement.
My house was built in 1969.