There are 2 things going on. Your soil has not been amended and therefore, has little bio-diversity to feed your plants. And, it's probably HIGHLY compacted. When gardeners are talking about "no-till" methods of planting, they mean, don't constantly till, put in your seedlings (or seeds) and leave an empty desert around them. If the dirt is literally hard as cement, ONLY the toughest weeds can penetrate it with their roots. Your vegetables have no chance. You must till to start amending your soil. I recommend raised beds bc you don't walk on them, and therefore, your plants can stretch their roots out.
I live on 5 acres of what was once a 50 acre farm, since subdivided. My horses continue to compact their 4 acres of pasture. Before that, one of the previous owners raised young steers, grazed them on the 5 acres surrounding the house and sold them in the fall. ALL of my 5 acres were highly compacted when I bought the property. For my GARDENING I own a good tiller, and I do use it. I also pile up what I clean from my horses from their stalls (they are stalled November-April) and their shelter and use it for my gardening, along with waste from my chickens. In the winter my beds get blanketed with manure and bedding bc it takes about 4 months to begin to break down and I don't want to burn my crops, although roses loves fresh horse manure.
You can bring in your compost and replace your dirt with it. It's a little late for the 2012 gardening season, but you can prepare for next year by composting THIS year.
Get on the phone and find a close-by horse stable. Ask where their manure pile is and locate the oldest debri. Ask them for grain bags, which are almost all plastic now, and volunteer to fill them yourself. You can tape them closed with duct tape and prevent it from spilling in your car. You need to mix THIS with your dirt, but you will get instant compost. Few plants will grow in the manure & bedding straight, but I had a volunteer pumpkin that came up in April from one of MY piles that was on top of last year's pumpkin patch, after I had tilled it.