Answer: It sounds as though your soil will barely support life! If you're serious about vegetable gardening you'll have to do some serious rehabilitation of your soil! Vegetable plant roots will grow 8"-12" deep in good soil, and the deeper the better. Strong root systems provide the plants with support, plus give them access to necessary water and nutrients. If your soil is impossible to work, how about gardening in raised beds? These can be formal beds with wood or concrete sides, or simply mounds of soil with no sides. You can purchase topsoil to fill the structures and amend it with organic matter such as aged-compost, leaf mold or peat moss. Dig as deeply as possible to loosen the soil and make it easier for the roots to penetrate. Then plant, water well, and harvest your bumper crop of veggies.
If you can't bring in topsoil and your soil is impossible to work, consider raising vegetables in containers on a sunny deck or patio. As long as the containers are 12" - 18" deep, have good drainage, and are filled with good potting soil, you'll be able to grow almost any vegetable you'd like.
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