ph is off
Did you do the soil test yourself or send it out to a lab? We'd recommend that you have a professional soil test lab test this soil. Home pH kits often get off-kilter and give false results. You can find a tab for soil testing info on the right side of our homepage.
What would account for such high pH readings? These are almost at a caustic level and certainly would account for crop problems. Once you have accurate pH readings, you can reduce the pH with sulfur. However, for us to tell you how much sulfur to use, we must have an accurate pH reading.
Vegetable gardens pH should be: http://extension.umd.edu/growit/food-gardening-101/step-3-prepare-your-soil
You DO NOT want to lime most of your garden. Lime will make the pH even higher and cause more problems in the high pH areas.
In the low pH areas, you may be able to lime a little. But there again, we'd need to know the exact pH in order to give you a lime recommendation. We assume that the high and lower pH areas are not near each other, right?