I have lived in and with field stone foundations most of my life. They were the best they had to work with 100 years ago and most of the time they never were water tight. If the water got in right after a heavy rain I would say it was most likely the rain and secondly the condensation. Some of the stones can appear to be sweating if water is working its way in around or thru them.
Before I started digging I would do a few above ground inspections. First is drain pipes from the gutters. The more you can get the water away from the foundation the better. The second thing to look at is grading. Old houses have a way of getting lots of stuff growing around the foundation walls and with lawns building up outside the landscaping you might have water collection points near the walls. Old plantings close to the foundations will also work roots down into the cracks of the field stones.
I had a water tank rust out and fail that was a good 4 feet from the outer wall. When I removed the tank I couldn’t believe my eyes but tree roots had come under the basement floor and up thru cracks and entered the bottom of the tank looking for water.
Rule out all the simple things first before digging. Then decide what you want to use the basement space for. Sometimes a sump and a few drain lines and a dehumidifier gets the job done. The correct repair if you want the space as a living area could be very expensive.