Start with the simple, and work towards the complex.
Have you verified the choke is working? Without choke, a cold engine won't idle. My '79 K was rather cold-blooded, requiring choke for a few minutes.
We know you have a working electrical system (it starts, it rev's), we know you have fuel reaching the cylinders (it starts, it rev's).
Known good gasoline in the tank? Not old, like from last riding season, or even older?
Is there a working, known good fuel filter in place? Crud from the tank could make its way down to the floats, or the carb jets, so a filter is always a good idea. Many of the OEM wire mesh filters ended up being removed from the petcock, leaving no filter in the system.
Can you give more details on what it does do? Will it remain running as long as you hold the throttle open a bit? Careful not to rev too high/too long without a load on the engine; keep it below 4,000 RPM to be safe.
Do you have proper weight oil in the engine? Oil of 10W-40 weight is good, but a 50 weight will make it more difficult to turn over due to the high viscosity --
very doubtful this is the real problem, but it's always worth checking the oil (amount, quality, and filter's condition).
Let us know more details, and we will be happy to offer suggestions. By the way, since you are new here, be sure to download the FSM (Factory Service Manual) from the home page. Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII