Hi and thank you for your question.
Just to make sure I understand you correctly, you bought a 2009 FZ-6 that had been totaled out and will not rev above an idle. If that is not correct, please let me know what I interpreted incorrectly. I would also like to know why the bike was totaled out. Usually it is because the bike has been crashed and the repair costs exceed 80% of the retail value of the bike. If it was crashed, please describe what damage the bike has, or had if you have done any crash repairs on it so far. One last detail about that, has the bike had this same symptom from the very first time you tried to start it or did it develop this problem after awhile?
As far as the running problem, does it start in what would seem to be normal? Fairly quick and easy? Does the engine seem to have any unusual noises that it is making while idling?
It also sounds like you are not getting any "check engine" warning lights either.
If everything seems pretty normal, I would suggest your next step be performing a compression test on the engine. Almost all of the time if you have a fuel or ignition problem it would throw a code and the check engine light would come on. None of the mechanical systems are included in those self diagnostics and that is what is leading me to look in other areas.
If you wouldn't mind, please fill me in on the answers to those questions and we can proceed forward with the diagnosis and repair of your motorcycle.