Get a post hole digger, the type that you turn with a cross handle as
it goes into the ground, not the style with two halves that you bring
together. With one of those and some extension pipe added on, you can
dig a hole probably 15 ft deep or so, certainly deep enough to
determine if the water level is above or below your basement level. Of
course, that assumes you live in an area with reasonable soil, not on a
mountain full of rocks.