If your "business" is writing Hub Pages, it's free and you definitely can.
If you are opening a commissioned sales business operated from your home or a table at an internet cafe, you may only need web page or business card and initiative. That too could be started for under $500.
If you are starting a business needing office space, licenses, inventory, insurance and incorporation then likely you cannot. Even then it depends what part of the world you're in and the purchasing power of the dollar there.
Many entrepreneurs outside the US seem to be able to significantly expand or start a business with under $500 through local banks or groups like Grameen.