I've had kind of the same issue over the last year and if it's an 02, the problem could be that the wiring everywhere will be getting old and corroded.
Just recently, my 01 had been running rough, coughing a bit at low revs and generally feeling woolly, and also being a bitch to start after cleaning it. I thought the carbs needed balancing again. Finally I had one cylinder not firing at all after a good scrub and wash, and as I was fiddling about trying to find the cause, I had a plug lead pull out of the plug cap. No resistance, just pulled straight out.
Now, remembering Falcon's advice (thanks!) about the ends of the plug leads getting hard with age, I snipped off half a centimetre of plug lead and hey presto, 4 cylinders. I thought I might as well check the others and they were all very loose and the plugs caps wouldn't tighten up when I screwed them in, so I snipped each plug lead, screwed them all back in tight and guess what - one smooth running, pokey Fazer again.
I wouldn't have believed it if someone had told me it would make that much difference. No more woolliness, not more coughing. It was almost like Ivanising it again. The weird thing is, it had been running kind of ok otherwise. Once it caught on all four, it was generally fine.
My bet's electrics. Check back from the plugs themselves - are the plugs all in tight (I had one pop clean out of the cylinder once!), then plug leads - as you screw them on can you feel them get tight, then take a look at how the connections are looking on the ignition coils, and if are they looking corroded give them a scrape, and keep going all the way back to the white connector underneath the tank. Mine fell apart earlier this year, so that's an important one to check, although that would cut all the electrics and send your alarm into a fit (I had to reset my Datatool after that. Oh, that was fun. Not!)
Still, it's all pretty easily fixable with methodical approach and a bit of patience. I'd be surprised if it's the carbs and a month's layup isn't anywhere near long enough for the fuel to go off.