Sounds like your getting sparks and fuel to the pots, so they can't be getting there at the right time or in the right amount.
As the only thing thats been done is to leave it for a few weeks then the timing or anything like that can't have changed.
Have you checked the choke mechanism hasn't siezed up during the layup?
Or how about the fuel filter being blocked?
I'd be surprised if the carbs have gummed up after 5 weeks.
Its going to be something simple that you'll kick yourself about.
I once changed the fuel filter on a motorbike after its winter layup and spent days trying to start it, I took everything apart and checked it, except take the filter back out and put it in the right way up so it didn't cause an airlock