"The ground here is like clay and we can't grow a proper garden, and we can't afford to move."
There are alternatives for planting. You can do raised beds or large containers. You will have to work the soil, there's plenty of info out there.
I plant on my patio now using containers. I plant tomatoes, lettuce, basil, celery, parsley, oregano, thyme. And this spring I will plant more. I try different things to see what does well. There may be free workshops in your area that can help you plan your garden
Here is a video that I find very inspiring--enjoy:
http://www.youtube.com/watch?v=mCPEBM5ol0Q
and my youtube channel devoted to home gardens~~
http://www.youtube.com/user/TheGardenista#p/f