Unless the engine starts, the computer will send a signal to the pump to preprime the pump and then shut it off. Once the computer acknowledge that the engine is running it will continue to send a signal to the pump to run. Sound like it's doing what it is suppose to do.
Do you have a CEL or SES or MIL? If you do you need to scan for the trouble code. That will tell you what the problem is. If the pump is energizing and the preprime procedure is occurring I would look to see if you have a spark. Could also be that you might have flooded the engine in your attempts at trying to start the engine. On the previous time that this happened to you you let the engine sit and if the engine was flooded, letting the engine sit will allow any gasoline to evaporate into a vapor. It's the vapor that is explosive, not the wet gasoline.