What's your definition of a business? In some states, just claiming your business a business by means of a business license will be over your $100 budget.
Now, if you want to make some money and get started, there's a ton of things you can do to get going, you've just got to get creative and use your resources. Resources such as time, knowing the right people to get deals or "ins", or already having a skillset you can apply, will be very helpful when starting with this minimal of a budget.
Remember it goes the other way too. You can have all the money in the world and fail. Say you have $100k and want to start a hobby shop in a high rent area, next to Walmart, expect high margins, don't have anything unique to offer, and have poor customer service. Think you'll make it? In the same respect, you've got guys out on the street performing banging on drums and dancing, and they're doing what they like, and getting by in their "business". I'm sure their drum sticks and budgets were well under $100.
Just be patient, work hard, get creative, and don't give up, and I think you can make that $100 work for you. There's been stories of people starting with $0 and made a lot of out themselves. I'd say you've got a good start on those people, but it's up to you to make it. Start shaking hands, kissing babies, buy low, and sell high, and you can make it...