my neighbor has a eunique problem. He owns a small home near the street. (within 10')The city repaved the street raising it above the level of his basement floor. (6")When it rains water runs back into his basement. How can he drain or rerout this water since the street pavement is there and he cannot cut through it. His back yard is slanted and has a patio that wraps around his home making things worse.

You could go with a sump pump system. I would suggest calling the city first and ask them for help. Some cities will work with you. Just remember the only time people call the city is because their mad. So be very nice and ask for the city engineer.