my Homelite Trimmer won't run after cranking?

I have a practically new Homelite String Trimmer (model #UT20006 25cc) that has been sitting in the box in my mother-in-law's closet for over 3 years. It will start up like a charm. Fairly easy to crank in the conventional manner. It will run fine for about 5-10 seconds, then shut off like it's starving for fuel. I can keep it running for a few more seconds by babying the throttle back and forth between half and full choke but it'll die every time. The fuel lines are fine...the fuel pickup is fine...the primer seems to work fine...the air filter is clean and the spark plug is fine. What in the heck could it be? Any suggestions would be greatly appreciated. THANKS!!!