Check your motor oil level?
Really, having the correct model and serial number series is "a must have" to be able to give you more correct information, but it would seem to me what is most likely happening is that the fuel lock-off is getting power during the 'cranking' phase, when the key switch is in start and starter engaged, but then runs out of that fuel when the key is moved to the 'run' position. You should be able to test that with a test light or meter at the lock-off. some units have an optional oil pressure shutdown system that will do this if you don't have motor oil. [among a lot of other possibilities]