I am not sure what kind of business you are looking to start but here are two possible solutions.
1. You could create an e-commerce, online or virtual business where location does not matter.
2. You could see what your small city or village needs and what you could provide that fills a gap in the market.
To create awareness of your small business/start up, you could try get local media coverage and use local social media.
Hope that helps!
it really comes down to the limits and based on your question the limits are pretty set in stone. If you are looking for a business that only trades locally to that small village you really want to make sure you know what the locals want on a regular basis. Selling "one time" items is going to dry up quickly so consumables would be ideal to ensure you have repeat business.
However I would never recommend anyone just setup a business with the mind set of a limited consumer base.
If you mean on the other hand what business can you start and run from a small village. Anything online comes to mind. Are there local products you can sell to the world, do you want to settup a drop ship account with a wholeseller and start selling world wide. So many options however I would recommend you do something you have a passion for. It makes it easier to press on when most would just walk away.
I think that Candice hit the nail on the head. However, I want to add that you should only start a business that you are personally passionate about. If you are not passionate, the business is not likely to succeed in the long-term because you need that passion to get through the ups and downs of business life. However, I think identifying gaps in your local market is a good starting point (only move forward with something you find interesting and/or exciting).