To get a dry basement, it is a two step process whether it is a modern
concrete basement or a field stone one.
You have addressed the first I think, by diverting the water coming off the hill on the upper side, but water will still be surrounding the walls by hydraulic pressure. To remove that you have to get the water that does get to your basement walls; out. In your case you would be better off to put a drain channel where your walls intersect with your floor and divert the water to daylight, which means running it down hill for however long it takes. This can be a trench or drainage tiles, but has to be of sufficient size to carry the volume of water you are getting on the inside of your basement.
It is easier said than done, because diverting the water to daylight can be wrought with other problems.