It could be something as simple as a discharged battery...in which case the battery would be such a drain that you get poor spark to the plugs. This is a possibility, but more likely than not the carbs are gummed up.
Relax...and it's really not that big of a deal. The hardest part is getting the carbs off and back on. (A little harder going on than off...it's getting the cables on that will give you some fits).
Since you already have the carbs off, there's really no reason to not clean the carbs. Get a couple of cans of carb cleaner at Wal-Mart....$5 total.
Here's a link to the 2001+ B6 manual:
http://www.gofastvideo.com/gallery/album/view/483/free-racing-videos/suzuki-service-manual.htmlTake your time; do one carb at a time, take pictures/notes as you take stuff apart. And wear safety glasses...the carb cleaner has a tendancy to shoot back!
Try to keep the carb cleaner off the rubber parts, like the diaphragms, but a little carb cleaner won't kill it.
It's a very gratifying thing to take a non-runner and bring it back to life. Do some reading this week, make a plan, and set aside this Saturday or Sunday to Git'r done!....and have fun, too.