Jamie;
My friend's Triumph had the very same issue a couple of years ago during attempted first starts after long layup...
Cause: It was lack of prime of the Fuel Pump...in your case, Blockages notwithstanding, first thing I'd recommend, is blowing some gentle positive pressure into the tank with an exhale, to encourage the fuel to the FuPu and beyond...remove output hose at Carbs and route into a catch can, and have a helper man the catch can as you make the pressure into the tankfiller. When helper announces fuel has made the trip, try starting...and watch for carb bowl overflows due to gummed Bowl Valves...not uncommon! I suggest you superclean those! See:
http://www.sw-em.com/SU%20Carb%20Ser...and_Bowlvalves
Good Hunting