Why did my herbs die?

I wanted a small, indoor herb garden. I planted basil, mint, lavender and Rosemary. They are about 4' away from a very sunny window other plants thrive in. They are all dying, within a week of planting. I watered them when I transplanted them, but not too much. Any idea on why their all dying so quickly, and any suggestions on what vegetables/herbs might actually grow indoors?