What is wrong if an 87 Nissan will not start unless starter fluid is sprayed into the carb while turning the key and then it dies?

Your Nissan obviously isn't getting any fuel to the carb. When you spray starting fluid to it it only allows it to run for a few seconds. First make sure your not out of gas in the tank. Next take the fuel line off the carb turn the engine over with the starter, if there is no fuel coming out of the fuel line then check and make sure your fuel filter isn't clogged. If filter is ok then your fuel pump probably needs replaced. Also make sure all of your fuel lines are ok and that there not blocked. More than likely your pump is bad.