The reason for more water in the basement is because of the large concrete surface installed outside of the home. The water is not longer allowed to perk into the soil evenly but is now concentrated in one location.
To handle the site issues I would have to look at the existing topography and to see the natural flow of water.
As for the ground water entering into the basement, the only solution would be to install perforated drain pipe with a geotextile cloth sleeve at the outside perimeter of the home and along the inside of the basement walls below the floor, both interconnected. These drains would need to be connected to a sump in the basement which would pump the water up and out.
I would recommend contacting a Civil engineer or Licensed Landscape Architect to assess the topography and site conditions. I would not recommend going to the expense of installing the drainage system until proper site drainage is established on the exterior of your home.
For more information:
Read "My lawn is lower than the lawns of the homes that surround me. What is the best strategy for keeping water out of my basement?" a Q&A answered by Elizabeth DiSalvo.