2002 model only 2900 miles running on one cylinder

Measure the battery voltage with the engine running. It should show a charge, 13+ volts on the battery. If not fault find the charging system.

probably old gas or condensation built up in carb or injectors.if carbureated drain float bowl & if you still have old gas in it drain tank close drain screw/bolt refill with premium fuel add fuel cleaner like b12 chemtool or seafoam(7-10$) to a fresh tank of gas...sometimes i just add the b12 chemtool (3-5$)and run it a few miles and it snaps right back to new!

Check fuel pressure. It should be in the region of 55 - 65 lbs.in After that ignition system needs to be checked. Does it run badly on both cylinders or just one? If one only then fuel pressure probably o/k.

I would double check the timing

It sounds like the float needle valves are lletting gas run into the bowl,in turn running gas into the motor,and fouling the spark plugs. Have you noticed if the oil level seems to be going UP,or the fuel level is going down? Kawasaki motorcycles are prone to leaking needle valves in the carbs for some reason. And the longer it sits,the worse its going to get.Try this,...pull the spark plugs and see if they are wet with fuel.Then,unhook the coils,and spin the motor over with the plugs out.If it shoots raw fuel about a foot out of each or ANY cylinder,then that is your problem. JUST BE SURE TO DISABLE THE COILS BEFORE SPINNING MOTOR OVER,AND DONT BE CLOSE TO THE PLUG HOLES WHEN YOU SPIN IT OVER!!
Good Luck!

First make certain the fuel is fresh ,and drain any old fuel out of the carb ,small screw at the bottom of the float bowl.when dry turn fuel on ,if flow starts again no blockage .start bike now,if no fix, remove spark plug if it is dry the carb is blocked . touch plug to cylinder head and start be carefull not to shock yourself use pliers . If no bright blue spark check side stand cut out switch ,kill switch . if the battery has been left uncharged for more than 2-3 months replace as wont work well. to check for seizure remove plug and push bike in first gear you should hear and feel the engine turn.

What happens when you try to accelerate?

Does the exhaust smell 'weird' when it's idling?

The most likely problem, especially with the bike sitting up during summer, would be gas has gone stale. If the bike sits long enough, the gas will actually turn into a varnish.

Drain the tank, refill with fresh gas, and let it run a while.
Basically, you have to run out whatever gas is between the tank and the cylinders, so the fresh gas can get to the cylinders.

I'd put a box fan blowing on the front of the bike to help keep the ehat down. Blip the throttle after a few inutes. Depending onhow much old gas is 'stored' in the fuel lines and such, it may take 10 or 20 minutes to burn out the old gas. Keep blipping every few minutes, and let it cool down after 20 minutes. Some bikes have short fuel path and clear in 2 minutes at idle, I've seen custom setups that took over an hour.

No the fuel pump will not fail more than once. When a fuel pump goes out it just goes. Will not work after that what so ever. Sounds like bad gas lines. I had this problem. I replaced my old gas line after the old one cracked when I did this I cut the new on to long. When I put my tank back on the old one pinched. It would run fine for a few min then sputter and die as the gas in the line ran out. I let it sit for a min and more gas filled the line and would start the process over. Try replacing the fuel lines and make sure they are cut to the right length and do not kink when the tank is on. It could also be a dirty petcock. I had let my bike sit for 6 months while in another state and the gat tank got dirty somehow. I got it running and same problem putters and dies. Neighbor took out the petcock and used an air hose to clean it out and it worked like new.

Take the carburetors apart and either rebuild them or clean them thoroughly.

Gas could be old, but it sounds more like you are losing spark to that cylinder at low rpm. Try a new spark plug, they're cheap. If that doesn't help, you could have a particle clogging the pilot jet of that carburetor. The pilot jet only works until you throttle it above idle. If it's clogged with a little junk, it will make bike idle terribly. Try spraying some carb cleaner through it (the one not running) with the engine on, and see if it likes the addition of fuel to that one cylinder. THis will tell you if you're lean on that jug. Good luck. Let me know. TT