I got a 02 cbr 600 f4i last year. Havn't had any problems out of it besides the battery. The guy before it said it was sitting for a couple months and so charged up the battery and it ran great. Havn't had any problems out of it besides the battery being dead if it sat over a week or 2 (Battery was bad I guess but doesn't hold charge long) Finally the battery just never charged anymore, I was push starting it for a month or 2 each time I rode it. (Never sat over a month rode it every so often through the winter.) One day I tried to push start it and I tried 5 times and it would just never start. Bought a new battery and installed it. It just cranks and cranks never starts. It's getting gas cause I can smell it. I guess it's not getting any spark but I'm not sure what to check for? I havn't changed anything and havn't rode it hard at all. I've googled for awhile trying to figure it out but havn't got a good answer, Figured i'd just post exactly what's been happening with it maybe someone can help me out!

 

could be a few things, the charging system might not be working, unlikely but, you never know. start by checking for spark.
for this you have to lean the tank back or remove it, remove the air box, and then its best to do it with a deep spark plug socket, a 1 inch swivel type connection and then a 2 inch extension i think, maybe 3.
anyways its for pulling the plug out instead of removing extensions as you go, you can just bend it and pull it out.
i have gently pried on the ignition coils and wiggle them a bit to help lift them up, with the handle of a socket wrench it helps remove them.
this is straight out of the manual
weak or no spark
faulty spark plug, fouled spark plug, faulty ecm, broken or shorted spark plug wire, faulty ignition switch
faulty ignition pulse generator, faulty engine stop switch, loose or disconnected ignition system wires.
on a side note i would never push start a bike but in emergency situations, it just seems like bad luck for me, cause i did that with a bike,
and next thing i knew i had magnets shreded off my flywheel all over my stator.

 

Sounds like the same problem I had with my Shadow a couple years ago, also had to push start it one day to get it home from work..in which it was acting all nutty ie: throttle kept cutting out, speedo was jumping around all over the place. The solution for that though was, simply replacing the battery as the old one was kaputt.
I'd definitely start by checking the plugs and if that doesn't work, go with what Rudy suggested.

 

Going to check the spark plugs first, as suggested. I got the seat and tank off atm. I noticed there's a plug on the box above the battery that's just sitting there not connected to anything. I don't think I remember it ever being connected to anything when I changed battery but I'll take a picture of it and post it just to see if anyone else knows.

 

Here's the picture (iphone pic)
What you're looking at is the orange is the gas tank, The right is the connectors to the ecu. There's a connector that looks like a 2 or 3 pin connector. (I just googled and looks like a diagnostics test connector.) Going to post it anyways just incase. Will continue to do spark plugs as soon as I get done with my car and update you guys when I do

 

that is what it is

 

That it is what? Test connector or the problem with my bike? I don't see anywhere for it to connect to.

 

Test connector is what "newb" means. I had wondered the same thing as, I noticed this green and orange wire myself a few days ago.

 

Ok good, So nothing that should be connected. I got the top air filter cover off, Velocity stacks off, air filter off, Now i'm trying to get the lower air box off. Looks like 3 hoses on back, 1 hose on front, and disconnect the 2 ram intake boxes and it should come out.

 

when you put it all back in there are 5 hoses that connect and 2 wire plugs, dont overlook them. 3 in the back 1 on the front and one on the clutch side into the map sensor.