My zzr 600 was running and then just quit. I

Check the idle, and seems to need a carburetor job, get iridium sparckplugst that will help too. But carb is the main reason

How long has the bike been sitting? Sounds like the carbs may be gummed up,and in need of a professional cleaning,and re-synchronizing.

The fuel system needs cleaning. Remove the carbs and petcock and clean them both out. The carbs have plugged jets which cause that. If you are not sure of how to properly clean out the carbs, I recommend that you take them to a shop or someone who knows how to.

Maybe needs a new radiator, thermostat, how is the water pump?I had this engine for 400.000km.

Im not sure about "bolt straight on" but it should be very close. most times bike models run for years without much major change. You may have to change a few brackets, or do a bit of bending and filing to get it to fit. The 06 ZZR has the twin headlights. I looked at some pictures carefully of the two different models. The frame is the same for both, so there is a good chance it will bolt straight on.

sounds like a carb or carbs are clogged need to have them cleaned and synced
may also want to make sure you have spark at all 4 cylinders

check float valve level could be sticking or shuting your fuel off also make sure you have good fuel flow from fuel valve

the firing order 1 2 4 3. from left to right as you sit on the bike, the leads are numberd..

I had a similar problem. Mine would continue running, but it felt like it dropped cylinders. Sputtered, backfires...etc. Check your ignitor box (under the seat, attached to the rear fender. Start the bike up to operating temp, and if it does the problem, the tech that fixed mine squeezed the ignitor box, and it returned to normal. Got a new one checking salvage yards online.

did you turn the fuel petcock back to the "on" position? ok that checks good step 2 maybe the filter is clogged. try changing the filter. or make sure that lack of fuel is causing the no start issue.