2001 450 es wont start

hello everyone it has been a very long time and a busy life but here I am with a new Honda and a new problem (to me) so we bought a 2001 450es and it was running rough with virtualy no high idle , so I cleaned the carb to no avail. then it decided to not start at all. so I disassembled the entire carb and installed a new rebuild kit from all balls. still no start. what it will do is spark and fire with backfire but ONLY while I am holding the starter button, it will run for 5 seconds then die after I release the starter button! all the grounds look ok and there are not burnt or broken wires anywhere , this is my daughters second Honda and we really want to get it running as good as I know it can before the riding season begins. btw my old 350 done gone and cracked a block so now it is waiting for a complete rebuild! I am almost at my wits end and ready to bite the bullet and take it to the shop!