Dry until basement was finished
I assume the "explosive nails" were Pasload or similar. They did not punch through the concrete, unless you had a REALLY narrow concrete wall, extraordinarily long nails, and the largest charge possible. Most likely the nails penetrated less than an inch into the concrete. I agree with previous posts, the nails likely had nothing to do with your problem.
As to solving a high water table problem, you need to make a careful evaluation of the cause of the problem. There are numerous posts on this forum over the last three years discussing causes and solutions to high groundwater issues, I suggest you do a search and begin reading. Retrofit solutions tend to be expensive and invasive, so should be done only after careful, thorough analysis of your specific situation, which may require installation of one or more groundwater monitoring devices (well, piezometer, test pit) so you can see how high the water table really gets, what kind of soil you have, and what system (if any) you already have in place to control groundwater.