It's said that necessity is the mother of invention, but it's also incentive to do some research about which vegetables can be re-grown on a countertop. It's really quite startling to see just how much can be grown from leftover scraps: all you need is water, and a sunny spot to place the plants, and within a week or two you'll have a fresh batch of edibles to enjoy.
Those wizened-looking roots of yours haven't gone bad: they're just dehydrated. You can revive them easily by immersing them in water for a few days.
Rather than being discouraged by the fact that I will never be able to grow a decent tomato here, I've learned the lesson that working with the land I have is easier on both my wallet and my heart than fighting with it.