Don't forget to supplement by going to any food pantries you can find. Go to your church, if you have one, and ask if they have a food pantry.
Post on your local Freecycle and ask for any garden extras that anyone might have. You never know when someone will say, "come on over and take all the oranges and plums from my trees" or "I have way too many peppers and cucumbers in my garden, please come take them."
Consider growing some food. Fairly recently, we spent about $4 on two small tomato plants, planted them in pots on our patio and about 3 weeks later, we already had tomatoes growing, delicious tomatoes. The tomatoes continued to grow faster than we could eat them, so we were able to give some away. Depending on your climate, there might be something similar you could grow that would be totally worth the initial cost.
As for that $100, look for sales in any flyers that you can and shop wisely. If you find packages of pasta, 2 for $1, buy them in bulk. Sit down and use a calendar sheet to plan your meals for the next 3 or 4 weeks, think about a varied menu (so you don't suffer much) and go from there.
In our family, a roast turkey can feed us for over a week, perhaps as much as 10 days. Try to find one on sale, perhaps for $10-12. It's a big job to make it but then you cut it up and wrap and freeze meal size portions of the meat for other meals. You can make soup from the carcass and turkey salad sandwiches from small turkey pieces that you pick off the bones. Make sure to stuff the turkey with stale cheap bread, add onions and celery and freeze servings of stuffing as well.
I find that oatmeal and cream of wheat is a cheaper breakfast than boxed cereals and very filling and nutritious. Make cookies once with the oatmeal and once with some flour and simple ingredients (sugar cookies or lemon cookies, for instance), having a simple treat every couple of weeks can really make simple meals feel extra special and can be really inexpensive.
Pancakes and waffles are inexpensive to make from scratch and can even be served at dinner.
Buy some stew meat, beef or chicken, on sale and cut it into really small pieces and use about half of what you would usually use to make a stew in your crockpot. Onions, celery, carrots and potatoes can be really cheap and add tons of good vitamins to your meal. Make mashed potatoes to pour the stew on and make sure to separate your stew into 3 sections and freeze the others for future meals.
20 lb bags of rice are life savers and can be used in so many ways, seasoned, or plain, and for different meals. I have made many a stirfry with $1 or 75 cents worth of vegetables poured over cooked rice for a family of 4. It's a matter of looking for sales, knowing when the prices are cheap and buying as much as you can when it's really cheap. Also, make sure you use every morsel of food and never let anything go bad before you use it.
Chicken and dumpings is a cheap and frugal meal to make. You don't need much chicken at all, so it's a great way to stretch what you have and make it seem like so much more.
Make soup from every bit of leftover vegetable and meat scraps that you have and serve it as often as you can.
When we are feeling deprived from eating on a very tight budget, we like to scour our cupboards and are sure to use every tea bag we can find and make iced tea with it. It's so nice to be able to look in the fridge and find special things to nibble on, like precut veggies, donated fruit and iced tea. If you can get some donated oranges or lemons, you might decide to make some lemonade or orange juice with them.
No matter what the budget, I would be sure to buy a cheap 10 lb bag of apples and buy a bunch of bananas and save money to repurchase those after a couple of weeks. A huge bag of carrots would always be in our cart, as well. You can eat them raw, put them in stews, cut them in small pieces and steam them, make creamed carrots from them, put some brown sugar on them and have sweet cooked carrots, etc. Very versatile.
I agree with the PP who suggested buying 5 lb blocks of cheese. You can cut them up into sections and freeze them. Used sparingly, you can really add such a richness to your diet and meals with cheese. Being able to make a baked pasta or lasagna, spreading it into two dishes and freezing one for later, is a good frugal meal. You can even incorporate any veggie leftovers that you have into the meal.
I would buy 4-8 loaves of bread on sale (less than a dollar a loaf) and freeze them. Sandwiches are a popular item in our family, jam sandwiches, peanut butter sandwiches, grilled cheese sandwiches, tuna, cinnamon toast in the mornings, etc. I would look for sales and buy numerous cans of tuna for cheap and plan tuna sandwiches for the family once per week.
Once you have your basic ingredients stocked up, you can check out
http://www.allrecipes.com to find varied recipes for your dinners. You can search for recipes according to what ingredients you have on hand, which is quite fun and very informative, too.
It doesn't hurt to keep your eyes and ears open and see if there are any free meals happening in your community...perhaps a local church is hosting a free meal, a friend might be having a party, the local community center might be hosting a free event, a family member might be willing to have your family over for dinner...
Good luck!