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If it is fairly minor, you could treat the interior of the wall with Thoroseal mixture before painting to avoid digging up the whole yard.
It is also a possibility that you are having condensation instead of leakage. Does this happen priomarily above ground level where the masonry is exposed to colder outside air? If that is the case, the cold surface is encouraging precipitation. Insulating the wall is the answer for that.
Finally, once the moisture problem is taken care of, you can paint the wall but any paint - especially primer - should be an alkyd made for masonry. It will state so on the can lable. Be sure the wall is clean and dry.