Try starting the engine by dropping a little fuel into the air filter, if it starts easily after that you know its a fuel problem and not an ignition problem.
If it's fuel, take the carbies off and check the fuel bowl is full, reset the float level, put back in bike, turn on, wait for the fuel pump to fill them up then take them off again and see if they are filling.
Here is some other advice for the carbies (but does not really affect whether the bike will start or not). Open the top of the carbies, the 2 circle caps with 4x screws each. Be careful and lift the black rubber diaphragm underneath, you will see two black plungers for each carby. The white plastic thing that hooks each plunger on don't last long so get a new set of 4:
http://www.suziparts.com.au/ p/n: 13511-38400, $5.
This area of the carby should be very clean and dry, if not - make it so

Unscrew the underside of the carby (the fuel bowls, clean them out and clean the rubber gasket being careful not to break it. Look for corrosion inside the brass jets, if they look bad get new ones or try and fix them with a drill bit of the same bore size.
If all that didnt work, maybe it needs the choke but your choke isnt working?
14m spanner to undo the two choke cables from the 2 carbies. Pull it all out, it should be the cable that sits in a brass housing, then a long spring and then a brass holder with a thin pin on the end which is all held together by the cable inner. Be careful cause its only being held together by the tension of the spring and it all falls apart very easily. To put it back in, assemble it and then gently slide it in, trying to feel the thin needle end is going into its home. When correctly installed you can hear it actuating when you open and close the choke from the handle bar if you put your ear near the carby with the engine off.
If dropping some fuel into the air filter didn't help, try measure the resistance of the ignition leads, if they are too high get new ones.
Take 1 spark plug out, reconnect its lead and then push the threaded part of the spark plug against the body of the bike, try and start the bike and watch the spark in the plug, should be small but bright white sparks.
I know this thread is old but I had the same problem with my bike, I am not sure which part cured it cause I did it all at the same time with new plugs and everything, just posting this if someone else stumbles across this thread.