Kinda hard to tell where it coming from, Most obvioius thing to me is the plumbing. make sure it not leaking. It looks fairly new. Is there and cracks in the wall near there? I cant really see in that picture.
I think you basically answered your own question.After making sure the gutters are clean, adding an extension to the downspout, I am reasonably sure the issue is the grading of the driveway.
I am wondering if, instead of having the driveway regraded completely, I might focus on the area within the black line. Maybe build it up and create a slope. Water seems to pool in this section and it is near this spot that the water is coming in, albeit at floor level in the basement.