My YTD snow blower has a Briggs and Straten engine. When I start the engine it will not run continuously. But if I pump the fuel injector buttom it will run. Could this be caused from fuel starvation? And if so how do I fix it without having to call or take it to a service center?

Yes, I would say you are correct and have a fuel delivery problem. How old is the fuel in the tank ? If you can empty it and replace with fresh that would be a good start. It is possible there is a blockage either in the fuel line or filter or with the carberetor itself. Some fuel cleaner additive such as Seafoam may also help.