2001 Suzuki Katana. Here is the story, after winter it fired up fine, just had a lag on the throttle. Pulled out air filter bike sounded like it loaded up and just died. I left it for a week. I went to fire it up and it just turns over. It will backfire and then nothing, just keeps turning over. I just replaced plugs I am getting gas as the float bowls are full. Battery holds charge great, it's only a year old. I have spark on all plugs, just won't start. Please help
Full float bowls don't necessarily mean a lot. Have you confirmed that you're getting gas to the plugs? Did you drain the float bowls before you laid the bike up for winter?
You need three things to get the engine running - fuel, spark and compression. Assuming that the timing isn't way off (which would also lead to backfiring), you've got a spark. Which leaves fuel or compression. It might be worth testing the compression but if you can feel the engine move air (ie, you can feel the pulses out the exhaust when cranking) I would assume the compression is still there, given that I assume the bike was running last year.
Which leaves the fuel. If you crank the engine for a little while, are the plugs wet afterwards? Or dry?
My guess is that the carbs are clogged from fuel deposits, especially if you haven't drained the bowls or run them dry. Here's what I'd do:
BTW, you did put the airfilter back in, didn't you? If the jetting is marginal already, the additional air from the lack of air filter might make the mixture too lean to fire properly on a cold engine.